1,1,25,0,0.0074164,"\int x^2 \left(a x^2+b x^3+c x^4\right) \, dx","Int[x^2*(a*x^2 + b*x^3 + c*x^4),x]","\frac{a x^5}{5}+\frac{b x^6}{6}+\frac{c x^7}{7}","\frac{a x^5}{5}+\frac{b x^6}{6}+\frac{c x^7}{7}",1,"(a*x^5)/5 + (b*x^6)/6 + (c*x^7)/7","A",2,1,20,0.05000,1,"{14}"
2,1,25,0,0.0073601,"\int x \left(a x^2+b x^3+c x^4\right) \, dx","Int[x*(a*x^2 + b*x^3 + c*x^4),x]","\frac{a x^4}{4}+\frac{b x^5}{5}+\frac{c x^6}{6}","\frac{a x^4}{4}+\frac{b x^5}{5}+\frac{c x^6}{6}",1,"(a*x^4)/4 + (b*x^5)/5 + (c*x^6)/6","A",2,1,18,0.05556,1,"{14}"
3,1,25,0,0.00384,"\int \left(a x^2+b x^3+c x^4\right) \, dx","Int[a*x^2 + b*x^3 + c*x^4,x]","\frac{a x^3}{3}+\frac{b x^4}{4}+\frac{c x^5}{5}","\frac{a x^3}{3}+\frac{b x^4}{4}+\frac{c x^5}{5}",1,"(a*x^3)/3 + (b*x^4)/4 + (c*x^5)/5","A",1,0,16,0,1,"{}"
4,1,25,0,0.0061748,"\int \frac{a x^2+b x^3+c x^4}{x} \, dx","Int[(a*x^2 + b*x^3 + c*x^4)/x,x]","\frac{a x^2}{2}+\frac{b x^3}{3}+\frac{c x^4}{4}","\frac{a x^2}{2}+\frac{b x^3}{3}+\frac{c x^4}{4}",1,"(a*x^2)/2 + (b*x^3)/3 + (c*x^4)/4","A",2,1,20,0.05000,1,"{14}"
5,1,20,0,0.0063249,"\int \frac{a x^2+b x^3+c x^4}{x^2} \, dx","Int[(a*x^2 + b*x^3 + c*x^4)/x^2,x]","a x+\frac{b x^2}{2}+\frac{c x^3}{3}","a x+\frac{b x^2}{2}+\frac{c x^3}{3}",1,"a*x + (b*x^2)/2 + (c*x^3)/3","A",2,1,20,0.05000,1,"{14}"
6,1,54,0,0.053594,"\int x^2 \left(a x^2+b x^3+c x^4\right)^2 \, dx","Int[x^2*(a*x^2 + b*x^3 + c*x^4)^2,x]","\frac{a^2 x^7}{7}+\frac{1}{9} x^9 \left(2 a c+b^2\right)+\frac{1}{4} a b x^8+\frac{1}{5} b c x^{10}+\frac{c^2 x^{11}}{11}","\frac{a^2 x^7}{7}+\frac{1}{9} x^9 \left(2 a c+b^2\right)+\frac{1}{4} a b x^8+\frac{1}{5} b c x^{10}+\frac{c^2 x^{11}}{11}",1,"(a^2*x^7)/7 + (a*b*x^8)/4 + ((b^2 + 2*a*c)*x^9)/9 + (b*c*x^10)/5 + (c^2*x^11)/11","A",3,2,22,0.09091,1,"{1585, 698}"
7,1,54,0,0.028877,"\int x \left(a x^2+b x^3+c x^4\right)^2 \, dx","Int[x*(a*x^2 + b*x^3 + c*x^4)^2,x]","\frac{a^2 x^6}{6}+\frac{1}{8} x^8 \left(2 a c+b^2\right)+\frac{2}{7} a b x^7+\frac{2}{9} b c x^9+\frac{c^2 x^{10}}{10}","\frac{a^2 x^6}{6}+\frac{1}{8} x^8 \left(2 a c+b^2\right)+\frac{2}{7} a b x^7+\frac{2}{9} b c x^9+\frac{c^2 x^{10}}{10}",1,"(a^2*x^6)/6 + (2*a*b*x^7)/7 + ((b^2 + 2*a*c)*x^8)/8 + (2*b*c*x^9)/9 + (c^2*x^10)/10","A",3,2,20,0.1000,1,"{1585, 698}"
8,1,54,0,0.0265261,"\int \left(a x^2+b x^3+c x^4\right)^2 \, dx","Int[(a*x^2 + b*x^3 + c*x^4)^2,x]","\frac{a^2 x^5}{5}+\frac{1}{7} x^7 \left(2 a c+b^2\right)+\frac{1}{3} a b x^6+\frac{1}{4} b c x^8+\frac{c^2 x^9}{9}","\frac{a^2 x^5}{5}+\frac{1}{7} x^7 \left(2 a c+b^2\right)+\frac{1}{3} a b x^6+\frac{1}{4} b c x^8+\frac{c^2 x^9}{9}",1,"(a^2*x^5)/5 + (a*b*x^6)/3 + ((b^2 + 2*a*c)*x^7)/7 + (b*c*x^8)/4 + (c^2*x^9)/9","A",3,2,18,0.1111,1,"{1594, 698}"
9,1,54,0,0.0320555,"\int \frac{\left(a x^2+b x^3+c x^4\right)^2}{x} \, dx","Int[(a*x^2 + b*x^3 + c*x^4)^2/x,x]","\frac{a^2 x^4}{4}+\frac{1}{6} x^6 \left(2 a c+b^2\right)+\frac{2}{5} a b x^5+\frac{2}{7} b c x^7+\frac{c^2 x^8}{8}","\frac{a^2 x^4}{4}+\frac{1}{6} x^6 \left(2 a c+b^2\right)+\frac{2}{5} a b x^5+\frac{2}{7} b c x^7+\frac{c^2 x^8}{8}",1,"(a^2*x^4)/4 + (2*a*b*x^5)/5 + ((b^2 + 2*a*c)*x^6)/6 + (2*b*c*x^7)/7 + (c^2*x^8)/8","A",3,2,22,0.09091,1,"{1585, 698}"
10,1,54,0,0.0324322,"\int \frac{\left(a x^2+b x^3+c x^4\right)^2}{x^2} \, dx","Int[(a*x^2 + b*x^3 + c*x^4)^2/x^2,x]","\frac{a^2 x^3}{3}+\frac{1}{5} x^5 \left(2 a c+b^2\right)+\frac{1}{2} a b x^4+\frac{1}{3} b c x^6+\frac{c^2 x^7}{7}","\frac{a^2 x^3}{3}+\frac{1}{5} x^5 \left(2 a c+b^2\right)+\frac{1}{2} a b x^4+\frac{1}{3} b c x^6+\frac{c^2 x^7}{7}",1,"(a^2*x^3)/3 + (a*b*x^4)/2 + ((b^2 + 2*a*c)*x^5)/5 + (b*c*x^6)/3 + (c^2*x^7)/7","A",3,2,22,0.09091,1,"{1585, 698}"
11,1,89,0,0.093805,"\int \frac{x^5}{a x^2+b x^3+c x^4} \, dx","Int[x^5/(a*x^2 + b*x^3 + c*x^4),x]","\frac{\left(b^2-a c\right) \log \left(a+b x+c x^2\right)}{2 c^3}+\frac{b \left(b^2-3 a c\right) \tanh ^{-1}\left(\frac{b+2 c x}{\sqrt{b^2-4 a c}}\right)}{c^3 \sqrt{b^2-4 a c}}-\frac{b x}{c^2}+\frac{x^2}{2 c}","\frac{\left(b^2-a c\right) \log \left(a+b x+c x^2\right)}{2 c^3}+\frac{b \left(b^2-3 a c\right) \tanh ^{-1}\left(\frac{b+2 c x}{\sqrt{b^2-4 a c}}\right)}{c^3 \sqrt{b^2-4 a c}}-\frac{b x}{c^2}+\frac{x^2}{2 c}",1,"-((b*x)/c^2) + x^2/(2*c) + (b*(b^2 - 3*a*c)*ArcTanh[(b + 2*c*x)/Sqrt[b^2 - 4*a*c]])/(c^3*Sqrt[b^2 - 4*a*c]) + ((b^2 - a*c)*Log[a + b*x + c*x^2])/(2*c^3)","A",7,6,22,0.2727,1,"{1585, 701, 634, 618, 206, 628}"
12,1,70,0,0.0587906,"\int \frac{x^4}{a x^2+b x^3+c x^4} \, dx","Int[x^4/(a*x^2 + b*x^3 + c*x^4),x]","-\frac{\left(b^2-2 a c\right) \tanh ^{-1}\left(\frac{b+2 c x}{\sqrt{b^2-4 a c}}\right)}{c^2 \sqrt{b^2-4 a c}}-\frac{b \log \left(a+b x+c x^2\right)}{2 c^2}+\frac{x}{c}","-\frac{\left(b^2-2 a c\right) \tanh ^{-1}\left(\frac{b+2 c x}{\sqrt{b^2-4 a c}}\right)}{c^2 \sqrt{b^2-4 a c}}-\frac{b \log \left(a+b x+c x^2\right)}{2 c^2}+\frac{x}{c}",1,"x/c - ((b^2 - 2*a*c)*ArcTanh[(b + 2*c*x)/Sqrt[b^2 - 4*a*c]])/(c^2*Sqrt[b^2 - 4*a*c]) - (b*Log[a + b*x + c*x^2])/(2*c^2)","A",6,6,22,0.2727,1,"{1585, 703, 634, 618, 206, 628}"
13,1,56,0,0.0395897,"\int \frac{x^3}{a x^2+b x^3+c x^4} \, dx","Int[x^3/(a*x^2 + b*x^3 + c*x^4),x]","\frac{b \tanh ^{-1}\left(\frac{b+2 c x}{\sqrt{b^2-4 a c}}\right)}{c \sqrt{b^2-4 a c}}+\frac{\log \left(a+b x+c x^2\right)}{2 c}","\frac{b \tanh ^{-1}\left(\frac{b+2 c x}{\sqrt{b^2-4 a c}}\right)}{c \sqrt{b^2-4 a c}}+\frac{\log \left(a+b x+c x^2\right)}{2 c}",1,"(b*ArcTanh[(b + 2*c*x)/Sqrt[b^2 - 4*a*c]])/(c*Sqrt[b^2 - 4*a*c]) + Log[a + b*x + c*x^2]/(2*c)","A",5,5,22,0.2273,1,"{1585, 634, 618, 206, 628}"
14,1,34,0,0.0259065,"\int \frac{x^2}{a x^2+b x^3+c x^4} \, dx","Int[x^2/(a*x^2 + b*x^3 + c*x^4),x]","-\frac{2 \tanh ^{-1}\left(\frac{b+2 c x}{\sqrt{b^2-4 a c}}\right)}{\sqrt{b^2-4 a c}}","-\frac{2 \tanh ^{-1}\left(\frac{b+2 c x}{\sqrt{b^2-4 a c}}\right)}{\sqrt{b^2-4 a c}}",1,"(-2*ArcTanh[(b + 2*c*x)/Sqrt[b^2 - 4*a*c]])/Sqrt[b^2 - 4*a*c]","A",3,3,22,0.1364,1,"{1585, 618, 206}"
15,1,62,0,0.0469107,"\int \frac{x}{a x^2+b x^3+c x^4} \, dx","Int[x/(a*x^2 + b*x^3 + c*x^4),x]","\frac{b \tanh ^{-1}\left(\frac{b+2 c x}{\sqrt{b^2-4 a c}}\right)}{a \sqrt{b^2-4 a c}}-\frac{\log \left(a+b x+c x^2\right)}{2 a}+\frac{\log (x)}{a}","\frac{b \tanh ^{-1}\left(\frac{b+2 c x}{\sqrt{b^2-4 a c}}\right)}{a \sqrt{b^2-4 a c}}-\frac{\log \left(a+b x+c x^2\right)}{2 a}+\frac{\log (x)}{a}",1,"(b*ArcTanh[(b + 2*c*x)/Sqrt[b^2 - 4*a*c]])/(a*Sqrt[b^2 - 4*a*c]) + Log[x]/a - Log[a + b*x + c*x^2]/(2*a)","A",7,7,20,0.3500,1,"{1585, 705, 29, 634, 618, 206, 628}"
16,1,81,0,0.0976829,"\int \frac{1}{a x^2+b x^3+c x^4} \, dx","Int[(a*x^2 + b*x^3 + c*x^4)^(-1),x]","-\frac{\left(b^2-2 a c\right) \tanh ^{-1}\left(\frac{b+2 c x}{\sqrt{b^2-4 a c}}\right)}{a^2 \sqrt{b^2-4 a c}}+\frac{b \log \left(a+b x+c x^2\right)}{2 a^2}-\frac{b \log (x)}{a^2}-\frac{1}{a x}","-\frac{\left(b^2-2 a c\right) \tanh ^{-1}\left(\frac{b+2 c x}{\sqrt{b^2-4 a c}}\right)}{a^2 \sqrt{b^2-4 a c}}+\frac{b \log \left(a+b x+c x^2\right)}{2 a^2}-\frac{b \log (x)}{a^2}-\frac{1}{a x}",1,"-(1/(a*x)) - ((b^2 - 2*a*c)*ArcTanh[(b + 2*c*x)/Sqrt[b^2 - 4*a*c]])/(a^2*Sqrt[b^2 - 4*a*c]) - (b*Log[x])/a^2 + (b*Log[a + b*x + c*x^2])/(2*a^2)","A",8,7,18,0.3889,1,"{1594, 709, 800, 634, 618, 206, 628}"
17,1,104,0,0.1459128,"\int \frac{1}{x \left(a x^2+b x^3+c x^4\right)} \, dx","Int[1/(x*(a*x^2 + b*x^3 + c*x^4)),x]","-\frac{\left(b^2-a c\right) \log \left(a+b x+c x^2\right)}{2 a^3}+\frac{\log (x) \left(b^2-a c\right)}{a^3}+\frac{b \left(b^2-3 a c\right) \tanh ^{-1}\left(\frac{b+2 c x}{\sqrt{b^2-4 a c}}\right)}{a^3 \sqrt{b^2-4 a c}}+\frac{b}{a^2 x}-\frac{1}{2 a x^2}","-\frac{\left(b^2-a c\right) \log \left(a+b x+c x^2\right)}{2 a^3}+\frac{\log (x) \left(b^2-a c\right)}{a^3}+\frac{b \left(b^2-3 a c\right) \tanh ^{-1}\left(\frac{b+2 c x}{\sqrt{b^2-4 a c}}\right)}{a^3 \sqrt{b^2-4 a c}}+\frac{b}{a^2 x}-\frac{1}{2 a x^2}",1,"-1/(2*a*x^2) + b/(a^2*x) + (b*(b^2 - 3*a*c)*ArcTanh[(b + 2*c*x)/Sqrt[b^2 - 4*a*c]])/(a^3*Sqrt[b^2 - 4*a*c]) + ((b^2 - a*c)*Log[x])/a^3 - ((b^2 - a*c)*Log[a + b*x + c*x^2])/(2*a^3)","A",8,7,22,0.3182,1,"{1585, 709, 800, 634, 618, 206, 628}"
18,1,137,0,0.202787,"\int \frac{1}{x^2 \left(a x^2+b x^3+c x^4\right)} \, dx","Int[1/(x^2*(a*x^2 + b*x^3 + c*x^4)),x]","-\frac{\left(2 a^2 c^2-4 a b^2 c+b^4\right) \tanh ^{-1}\left(\frac{b+2 c x}{\sqrt{b^2-4 a c}}\right)}{a^4 \sqrt{b^2-4 a c}}+\frac{b \left(b^2-2 a c\right) \log \left(a+b x+c x^2\right)}{2 a^4}-\frac{b^2-a c}{a^3 x}-\frac{b \log (x) \left(b^2-2 a c\right)}{a^4}+\frac{b}{2 a^2 x^2}-\frac{1}{3 a x^3}","-\frac{\left(2 a^2 c^2-4 a b^2 c+b^4\right) \tanh ^{-1}\left(\frac{b+2 c x}{\sqrt{b^2-4 a c}}\right)}{a^4 \sqrt{b^2-4 a c}}+\frac{b \left(b^2-2 a c\right) \log \left(a+b x+c x^2\right)}{2 a^4}-\frac{b^2-a c}{a^3 x}-\frac{b \log (x) \left(b^2-2 a c\right)}{a^4}+\frac{b}{2 a^2 x^2}-\frac{1}{3 a x^3}",1,"-1/(3*a*x^3) + b/(2*a^2*x^2) - (b^2 - a*c)/(a^3*x) - ((b^4 - 4*a*b^2*c + 2*a^2*c^2)*ArcTanh[(b + 2*c*x)/Sqrt[b^2 - 4*a*c]])/(a^4*Sqrt[b^2 - 4*a*c]) - (b*(b^2 - 2*a*c)*Log[x])/a^4 + (b*(b^2 - 2*a*c)*Log[a + b*x + c*x^2])/(2*a^4)","A",8,7,22,0.3182,1,"{1585, 709, 800, 634, 618, 206, 628}"
19,1,150,0,0.1592773,"\int \frac{x^8}{\left(a x^2+b x^3+c x^4\right)^2} \, dx","Int[x^8/(a*x^2 + b*x^3 + c*x^4)^2,x]","-\frac{2 \left(6 a^2 c^2-6 a b^2 c+b^4\right) \tanh ^{-1}\left(\frac{b+2 c x}{\sqrt{b^2-4 a c}}\right)}{c^3 \left(b^2-4 a c\right)^{3/2}}+\frac{2 x \left(b^2-3 a c\right)}{c^2 \left(b^2-4 a c\right)}+\frac{x^3 (2 a+b x)}{\left(b^2-4 a c\right) \left(a+b x+c x^2\right)}-\frac{b x^2}{c \left(b^2-4 a c\right)}-\frac{b \log \left(a+b x+c x^2\right)}{c^3}","-\frac{2 \left(6 a^2 c^2-6 a b^2 c+b^4\right) \tanh ^{-1}\left(\frac{b+2 c x}{\sqrt{b^2-4 a c}}\right)}{c^3 \left(b^2-4 a c\right)^{3/2}}+\frac{2 x \left(b^2-3 a c\right)}{c^2 \left(b^2-4 a c\right)}+\frac{x^3 (2 a+b x)}{\left(b^2-4 a c\right) \left(a+b x+c x^2\right)}-\frac{b x^2}{c \left(b^2-4 a c\right)}-\frac{b \log \left(a+b x+c x^2\right)}{c^3}",1,"(2*(b^2 - 3*a*c)*x)/(c^2*(b^2 - 4*a*c)) - (b*x^2)/(c*(b^2 - 4*a*c)) + (x^3*(2*a + b*x))/((b^2 - 4*a*c)*(a + b*x + c*x^2)) - (2*(b^4 - 6*a*b^2*c + 6*a^2*c^2)*ArcTanh[(b + 2*c*x)/Sqrt[b^2 - 4*a*c]])/(c^3*(b^2 - 4*a*c)^(3/2)) - (b*Log[a + b*x + c*x^2])/c^3","A",8,7,22,0.3182,1,"{1585, 738, 800, 634, 618, 206, 628}"
20,1,114,0,0.1032815,"\int \frac{x^7}{\left(a x^2+b x^3+c x^4\right)^2} \, dx","Int[x^7/(a*x^2 + b*x^3 + c*x^4)^2,x]","\frac{b \left(b^2-6 a c\right) \tanh ^{-1}\left(\frac{b+2 c x}{\sqrt{b^2-4 a c}}\right)}{c^2 \left(b^2-4 a c\right)^{3/2}}+\frac{x^2 (2 a+b x)}{\left(b^2-4 a c\right) \left(a+b x+c x^2\right)}-\frac{b x}{c \left(b^2-4 a c\right)}+\frac{\log \left(a+b x+c x^2\right)}{2 c^2}","\frac{b \left(b^2-6 a c\right) \tanh ^{-1}\left(\frac{b+2 c x}{\sqrt{b^2-4 a c}}\right)}{c^2 \left(b^2-4 a c\right)^{3/2}}+\frac{x^2 (2 a+b x)}{\left(b^2-4 a c\right) \left(a+b x+c x^2\right)}-\frac{b x}{c \left(b^2-4 a c\right)}+\frac{\log \left(a+b x+c x^2\right)}{2 c^2}",1,"-((b*x)/(c*(b^2 - 4*a*c))) + (x^2*(2*a + b*x))/((b^2 - 4*a*c)*(a + b*x + c*x^2)) + (b*(b^2 - 6*a*c)*ArcTanh[(b + 2*c*x)/Sqrt[b^2 - 4*a*c]])/(c^2*(b^2 - 4*a*c)^(3/2)) + Log[a + b*x + c*x^2]/(2*c^2)","A",7,7,22,0.3182,1,"{1585, 738, 773, 634, 618, 206, 628}"
21,1,67,0,0.0391678,"\int \frac{x^6}{\left(a x^2+b x^3+c x^4\right)^2} \, dx","Int[x^6/(a*x^2 + b*x^3 + c*x^4)^2,x]","\frac{x (2 a+b x)}{\left(b^2-4 a c\right) \left(a+b x+c x^2\right)}+\frac{4 a \tanh ^{-1}\left(\frac{b+2 c x}{\sqrt{b^2-4 a c}}\right)}{\left(b^2-4 a c\right)^{3/2}}","\frac{x (2 a+b x)}{\left(b^2-4 a c\right) \left(a+b x+c x^2\right)}+\frac{4 a \tanh ^{-1}\left(\frac{b+2 c x}{\sqrt{b^2-4 a c}}\right)}{\left(b^2-4 a c\right)^{3/2}}",1,"(x*(2*a + b*x))/((b^2 - 4*a*c)*(a + b*x + c*x^2)) + (4*a*ArcTanh[(b + 2*c*x)/Sqrt[b^2 - 4*a*c]])/(b^2 - 4*a*c)^(3/2)","A",4,4,22,0.1818,1,"{1585, 722, 618, 206}"
22,1,66,0,0.0378451,"\int \frac{x^5}{\left(a x^2+b x^3+c x^4\right)^2} \, dx","Int[x^5/(a*x^2 + b*x^3 + c*x^4)^2,x]","\frac{2 a+b x}{\left(b^2-4 a c\right) \left(a+b x+c x^2\right)}-\frac{2 b \tanh ^{-1}\left(\frac{b+2 c x}{\sqrt{b^2-4 a c}}\right)}{\left(b^2-4 a c\right)^{3/2}}","\frac{2 a+b x}{\left(b^2-4 a c\right) \left(a+b x+c x^2\right)}-\frac{2 b \tanh ^{-1}\left(\frac{b+2 c x}{\sqrt{b^2-4 a c}}\right)}{\left(b^2-4 a c\right)^{3/2}}",1,"(2*a + b*x)/((b^2 - 4*a*c)*(a + b*x + c*x^2)) - (2*b*ArcTanh[(b + 2*c*x)/Sqrt[b^2 - 4*a*c]])/(b^2 - 4*a*c)^(3/2)","A",4,4,22,0.1818,1,"{1585, 638, 618, 206}"
23,1,66,0,0.0345985,"\int \frac{x^4}{\left(a x^2+b x^3+c x^4\right)^2} \, dx","Int[x^4/(a*x^2 + b*x^3 + c*x^4)^2,x]","\frac{4 c \tanh ^{-1}\left(\frac{b+2 c x}{\sqrt{b^2-4 a c}}\right)}{\left(b^2-4 a c\right)^{3/2}}-\frac{b+2 c x}{\left(b^2-4 a c\right) \left(a+b x+c x^2\right)}","\frac{4 c \tanh ^{-1}\left(\frac{b+2 c x}{\sqrt{b^2-4 a c}}\right)}{\left(b^2-4 a c\right)^{3/2}}-\frac{b+2 c x}{\left(b^2-4 a c\right) \left(a+b x+c x^2\right)}",1,"-((b + 2*c*x)/((b^2 - 4*a*c)*(a + b*x + c*x^2))) + (4*c*ArcTanh[(b + 2*c*x)/Sqrt[b^2 - 4*a*c]])/(b^2 - 4*a*c)^(3/2)","A",4,4,22,0.1818,1,"{1585, 614, 618, 206}"
24,1,108,0,0.148149,"\int \frac{x^3}{\left(a x^2+b x^3+c x^4\right)^2} \, dx","Int[x^3/(a*x^2 + b*x^3 + c*x^4)^2,x]","\frac{b \left(b^2-6 a c\right) \tanh ^{-1}\left(\frac{b+2 c x}{\sqrt{b^2-4 a c}}\right)}{a^2 \left(b^2-4 a c\right)^{3/2}}-\frac{\log \left(a+b x+c x^2\right)}{2 a^2}+\frac{\log (x)}{a^2}+\frac{-2 a c+b^2+b c x}{a \left(b^2-4 a c\right) \left(a+b x+c x^2\right)}","\frac{b \left(b^2-6 a c\right) \tanh ^{-1}\left(\frac{b+2 c x}{\sqrt{b^2-4 a c}}\right)}{a^2 \left(b^2-4 a c\right)^{3/2}}-\frac{\log \left(a+b x+c x^2\right)}{2 a^2}+\frac{\log (x)}{a^2}+\frac{-2 a c+b^2+b c x}{a \left(b^2-4 a c\right) \left(a+b x+c x^2\right)}",1,"(b^2 - 2*a*c + b*c*x)/(a*(b^2 - 4*a*c)*(a + b*x + c*x^2)) + (b*(b^2 - 6*a*c)*ArcTanh[(b + 2*c*x)/Sqrt[b^2 - 4*a*c]])/(a^2*(b^2 - 4*a*c)^(3/2)) + Log[x]/a^2 - Log[a + b*x + c*x^2]/(2*a^2)","A",8,7,22,0.3182,1,"{1585, 740, 800, 634, 618, 206, 628}"
25,1,148,0,0.1980255,"\int \frac{x^2}{\left(a x^2+b x^3+c x^4\right)^2} \, dx","Int[x^2/(a*x^2 + b*x^3 + c*x^4)^2,x]","-\frac{2 \left(6 a^2 c^2-6 a b^2 c+b^4\right) \tanh ^{-1}\left(\frac{b+2 c x}{\sqrt{b^2-4 a c}}\right)}{a^3 \left(b^2-4 a c\right)^{3/2}}-\frac{2 \left(b^2-3 a c\right)}{a^2 x \left(b^2-4 a c\right)}+\frac{b \log \left(a+b x+c x^2\right)}{a^3}-\frac{2 b \log (x)}{a^3}+\frac{-2 a c+b^2+b c x}{a x \left(b^2-4 a c\right) \left(a+b x+c x^2\right)}","-\frac{2 \left(6 a^2 c^2-6 a b^2 c+b^4\right) \tanh ^{-1}\left(\frac{b+2 c x}{\sqrt{b^2-4 a c}}\right)}{a^3 \left(b^2-4 a c\right)^{3/2}}-\frac{2 \left(b^2-3 a c\right)}{a^2 x \left(b^2-4 a c\right)}+\frac{b \log \left(a+b x+c x^2\right)}{a^3}-\frac{2 b \log (x)}{a^3}+\frac{-2 a c+b^2+b c x}{a x \left(b^2-4 a c\right) \left(a+b x+c x^2\right)}",1,"(-2*(b^2 - 3*a*c))/(a^2*(b^2 - 4*a*c)*x) + (b^2 - 2*a*c + b*c*x)/(a*(b^2 - 4*a*c)*x*(a + b*x + c*x^2)) - (2*(b^4 - 6*a*b^2*c + 6*a^2*c^2)*ArcTanh[(b + 2*c*x)/Sqrt[b^2 - 4*a*c]])/(a^3*(b^2 - 4*a*c)^(3/2)) - (2*b*Log[x])/a^3 + (b*Log[a + b*x + c*x^2])/a^3","A",8,7,22,0.3182,1,"{1585, 740, 800, 634, 618, 206, 628}"
26,1,202,0,0.2502972,"\int \frac{x}{\left(a x^2+b x^3+c x^4\right)^2} \, dx","Int[x/(a*x^2 + b*x^3 + c*x^4)^2,x]","\frac{b \left(30 a^2 c^2-20 a b^2 c+3 b^4\right) \tanh ^{-1}\left(\frac{b+2 c x}{\sqrt{b^2-4 a c}}\right)}{a^4 \left(b^2-4 a c\right)^{3/2}}-\frac{3 b^2-8 a c}{2 a^2 x^2 \left(b^2-4 a c\right)}-\frac{\left(3 b^2-2 a c\right) \log \left(a+b x+c x^2\right)}{2 a^4}+\frac{b \left(3 b^2-11 a c\right)}{a^3 x \left(b^2-4 a c\right)}+\frac{\log (x) \left(3 b^2-2 a c\right)}{a^4}+\frac{-2 a c+b^2+b c x}{a x^2 \left(b^2-4 a c\right) \left(a+b x+c x^2\right)}","\frac{b \left(30 a^2 c^2-20 a b^2 c+3 b^4\right) \tanh ^{-1}\left(\frac{b+2 c x}{\sqrt{b^2-4 a c}}\right)}{a^4 \left(b^2-4 a c\right)^{3/2}}-\frac{3 b^2-8 a c}{2 a^2 x^2 \left(b^2-4 a c\right)}-\frac{\left(3 b^2-2 a c\right) \log \left(a+b x+c x^2\right)}{2 a^4}+\frac{b \left(3 b^2-11 a c\right)}{a^3 x \left(b^2-4 a c\right)}+\frac{\log (x) \left(3 b^2-2 a c\right)}{a^4}+\frac{-2 a c+b^2+b c x}{a x^2 \left(b^2-4 a c\right) \left(a+b x+c x^2\right)}",1,"-(3*b^2 - 8*a*c)/(2*a^2*(b^2 - 4*a*c)*x^2) + (b*(3*b^2 - 11*a*c))/(a^3*(b^2 - 4*a*c)*x) + (b^2 - 2*a*c + b*c*x)/(a*(b^2 - 4*a*c)*x^2*(a + b*x + c*x^2)) + (b*(3*b^4 - 20*a*b^2*c + 30*a^2*c^2)*ArcTanh[(b + 2*c*x)/Sqrt[b^2 - 4*a*c]])/(a^4*(b^2 - 4*a*c)^(3/2)) + ((3*b^2 - 2*a*c)*Log[x])/a^4 - ((3*b^2 - 2*a*c)*Log[a + b*x + c*x^2])/(2*a^4)","A",8,7,20,0.3500,1,"{1585, 740, 800, 634, 618, 206, 628}"
27,1,252,0,0.3233369,"\int \frac{1}{\left(a x^2+b x^3+c x^4\right)^2} \, dx","Int[(a*x^2 + b*x^3 + c*x^4)^(-2),x]","-\frac{2 \left(5 a^2 c^2-9 a b^2 c+2 b^4\right)}{a^4 x \left(b^2-4 a c\right)}-\frac{2 \left(30 a^2 b^2 c^2-10 a^3 c^3-15 a b^4 c+2 b^6\right) \tanh ^{-1}\left(\frac{b+2 c x}{\sqrt{b^2-4 a c}}\right)}{a^5 \left(b^2-4 a c\right)^{3/2}}+\frac{b \left(2 b^2-7 a c\right)}{a^3 x^2 \left(b^2-4 a c\right)}-\frac{2 \left(2 b^2-5 a c\right)}{3 a^2 x^3 \left(b^2-4 a c\right)}+\frac{b \left(2 b^2-3 a c\right) \log \left(a+b x+c x^2\right)}{a^5}-\frac{2 b \log (x) \left(2 b^2-3 a c\right)}{a^5}+\frac{-2 a c+b^2+b c x}{a x^3 \left(b^2-4 a c\right) \left(a+b x+c x^2\right)}","-\frac{2 \left(5 a^2 c^2-9 a b^2 c+2 b^4\right)}{a^4 x \left(b^2-4 a c\right)}-\frac{2 \left(30 a^2 b^2 c^2-10 a^3 c^3-15 a b^4 c+2 b^6\right) \tanh ^{-1}\left(\frac{b+2 c x}{\sqrt{b^2-4 a c}}\right)}{a^5 \left(b^2-4 a c\right)^{3/2}}+\frac{b \left(2 b^2-7 a c\right)}{a^3 x^2 \left(b^2-4 a c\right)}-\frac{2 \left(2 b^2-5 a c\right)}{3 a^2 x^3 \left(b^2-4 a c\right)}+\frac{b \left(2 b^2-3 a c\right) \log \left(a+b x+c x^2\right)}{a^5}-\frac{2 b \log (x) \left(2 b^2-3 a c\right)}{a^5}+\frac{-2 a c+b^2+b c x}{a x^3 \left(b^2-4 a c\right) \left(a+b x+c x^2\right)}",1,"(-2*(2*b^2 - 5*a*c))/(3*a^2*(b^2 - 4*a*c)*x^3) + (b*(2*b^2 - 7*a*c))/(a^3*(b^2 - 4*a*c)*x^2) - (2*(2*b^4 - 9*a*b^2*c + 5*a^2*c^2))/(a^4*(b^2 - 4*a*c)*x) + (b^2 - 2*a*c + b*c*x)/(a*(b^2 - 4*a*c)*x^3*(a + b*x + c*x^2)) - (2*(2*b^6 - 15*a*b^4*c + 30*a^2*b^2*c^2 - 10*a^3*c^3)*ArcTanh[(b + 2*c*x)/Sqrt[b^2 - 4*a*c]])/(a^5*(b^2 - 4*a*c)^(3/2)) - (2*b*(2*b^2 - 3*a*c)*Log[x])/a^5 + (b*(2*b^2 - 3*a*c)*Log[a + b*x + c*x^2])/a^5","A",8,7,18,0.3889,1,"{1594, 740, 800, 634, 618, 206, 628}"
28,1,318,0,0.3918152,"\int \frac{1}{x \left(a x^2+b x^3+c x^4\right)^2} \, dx","Int[1/(x*(a*x^2 + b*x^3 + c*x^4)^2),x]","-\frac{12 a^2 c^2-22 a b^2 c+5 b^4}{2 a^4 x^2 \left(b^2-4 a c\right)}-\frac{\left(3 a^2 c^2-12 a b^2 c+5 b^4\right) \log \left(a+b x+c x^2\right)}{2 a^6}+\frac{b \left(29 a^2 c^2-27 a b^2 c+5 b^4\right)}{a^5 x \left(b^2-4 a c\right)}+\frac{\log (x) \left(3 a^2 c^2-12 a b^2 c+5 b^4\right)}{a^6}+\frac{b \left(105 a^2 b^2 c^2-70 a^3 c^3-42 a b^4 c+5 b^6\right) \tanh ^{-1}\left(\frac{b+2 c x}{\sqrt{b^2-4 a c}}\right)}{a^6 \left(b^2-4 a c\right)^{3/2}}+\frac{b \left(5 b^2-17 a c\right)}{3 a^3 x^3 \left(b^2-4 a c\right)}-\frac{5 b^2-12 a c}{4 a^2 x^4 \left(b^2-4 a c\right)}+\frac{-2 a c+b^2+b c x}{a x^4 \left(b^2-4 a c\right) \left(a+b x+c x^2\right)}","-\frac{12 a^2 c^2-22 a b^2 c+5 b^4}{2 a^4 x^2 \left(b^2-4 a c\right)}-\frac{\left(3 a^2 c^2-12 a b^2 c+5 b^4\right) \log \left(a+b x+c x^2\right)}{2 a^6}+\frac{b \left(29 a^2 c^2-27 a b^2 c+5 b^4\right)}{a^5 x \left(b^2-4 a c\right)}+\frac{\log (x) \left(3 a^2 c^2-12 a b^2 c+5 b^4\right)}{a^6}+\frac{b \left(105 a^2 b^2 c^2-70 a^3 c^3-42 a b^4 c+5 b^6\right) \tanh ^{-1}\left(\frac{b+2 c x}{\sqrt{b^2-4 a c}}\right)}{a^6 \left(b^2-4 a c\right)^{3/2}}+\frac{b \left(5 b^2-17 a c\right)}{3 a^3 x^3 \left(b^2-4 a c\right)}-\frac{5 b^2-12 a c}{4 a^2 x^4 \left(b^2-4 a c\right)}+\frac{-2 a c+b^2+b c x}{a x^4 \left(b^2-4 a c\right) \left(a+b x+c x^2\right)}",1,"-(5*b^2 - 12*a*c)/(4*a^2*(b^2 - 4*a*c)*x^4) + (b*(5*b^2 - 17*a*c))/(3*a^3*(b^2 - 4*a*c)*x^3) - (5*b^4 - 22*a*b^2*c + 12*a^2*c^2)/(2*a^4*(b^2 - 4*a*c)*x^2) + (b*(5*b^4 - 27*a*b^2*c + 29*a^2*c^2))/(a^5*(b^2 - 4*a*c)*x) + (b^2 - 2*a*c + b*c*x)/(a*(b^2 - 4*a*c)*x^4*(a + b*x + c*x^2)) + (b*(5*b^6 - 42*a*b^4*c + 105*a^2*b^2*c^2 - 70*a^3*c^3)*ArcTanh[(b + 2*c*x)/Sqrt[b^2 - 4*a*c]])/(a^6*(b^2 - 4*a*c)^(3/2)) + ((5*b^4 - 12*a*b^2*c + 3*a^2*c^2)*Log[x])/a^6 - ((5*b^4 - 12*a*b^2*c + 3*a^2*c^2)*Log[a + b*x + c*x^2])/(2*a^6)","A",8,7,22,0.3182,1,"{1585, 740, 800, 634, 618, 206, 628}"
29,1,257,0,0.5884407,"\int x^2 \sqrt{a x^2+b x^3+c x^4} \, dx","Int[x^2*Sqrt[a*x^2 + b*x^3 + c*x^4],x]","-\frac{\left(256 a^2 c^2-460 a b^2 c+105 b^4\right) \sqrt{a x^2+b x^3+c x^4}}{1920 c^4 x}-\frac{x \left(7 b^2-16 a c\right) \sqrt{a x^2+b x^3+c x^4}}{240 c^2}+\frac{b \left(35 b^2-116 a c\right) \sqrt{a x^2+b x^3+c x^4}}{960 c^3}+\frac{b x \left(7 b^2-12 a c\right) \left(b^2-4 a c\right) \sqrt{a+b x+c x^2} \tanh ^{-1}\left(\frac{b+2 c x}{2 \sqrt{c} \sqrt{a+b x+c x^2}}\right)}{256 c^{9/2} \sqrt{a x^2+b x^3+c x^4}}+\frac{x^2 (b+8 c x) \sqrt{a x^2+b x^3+c x^4}}{40 c}","-\frac{\left(256 a^2 c^2-460 a b^2 c+105 b^4\right) \sqrt{a x^2+b x^3+c x^4}}{1920 c^4 x}-\frac{x \left(7 b^2-16 a c\right) \sqrt{a x^2+b x^3+c x^4}}{240 c^2}+\frac{b \left(35 b^2-116 a c\right) \sqrt{a x^2+b x^3+c x^4}}{960 c^3}+\frac{b x \left(7 b^2-12 a c\right) \left(b^2-4 a c\right) \sqrt{a+b x+c x^2} \tanh ^{-1}\left(\frac{b+2 c x}{2 \sqrt{c} \sqrt{a+b x+c x^2}}\right)}{256 c^{9/2} \sqrt{a x^2+b x^3+c x^4}}+\frac{x^2 (b+8 c x) \sqrt{a x^2+b x^3+c x^4}}{40 c}",1,"(b*(35*b^2 - 116*a*c)*Sqrt[a*x^2 + b*x^3 + c*x^4])/(960*c^3) - ((105*b^4 - 460*a*b^2*c + 256*a^2*c^2)*Sqrt[a*x^2 + b*x^3 + c*x^4])/(1920*c^4*x) - ((7*b^2 - 16*a*c)*x*Sqrt[a*x^2 + b*x^3 + c*x^4])/(240*c^2) + (x^2*(b + 8*c*x)*Sqrt[a*x^2 + b*x^3 + c*x^4])/(40*c) + (b*(7*b^2 - 12*a*c)*(b^2 - 4*a*c)*x*Sqrt[a + b*x + c*x^2]*ArcTanh[(b + 2*c*x)/(2*Sqrt[c]*Sqrt[a + b*x + c*x^2])])/(256*c^(9/2)*Sqrt[a*x^2 + b*x^3 + c*x^4])","A",8,6,24,0.2500,1,"{1919, 1949, 12, 1914, 621, 206}"
30,1,205,0,0.3702739,"\int x \sqrt{a x^2+b x^3+c x^4} \, dx","Int[x*Sqrt[a*x^2 + b*x^3 + c*x^4],x]","\frac{b \left(15 b^2-52 a c\right) \sqrt{a x^2+b x^3+c x^4}}{192 c^3 x}-\frac{\left(5 b^2-12 a c\right) \sqrt{a x^2+b x^3+c x^4}}{96 c^2}-\frac{x \left(b^2-4 a c\right) \left(5 b^2-4 a c\right) \sqrt{a+b x+c x^2} \tanh ^{-1}\left(\frac{b+2 c x}{2 \sqrt{c} \sqrt{a+b x+c x^2}}\right)}{128 c^{7/2} \sqrt{a x^2+b x^3+c x^4}}+\frac{x (b+6 c x) \sqrt{a x^2+b x^3+c x^4}}{24 c}","\frac{b \left(15 b^2-52 a c\right) \sqrt{a x^2+b x^3+c x^4}}{192 c^3 x}-\frac{\left(5 b^2-12 a c\right) \sqrt{a x^2+b x^3+c x^4}}{96 c^2}-\frac{x \left(b^2-4 a c\right) \left(5 b^2-4 a c\right) \sqrt{a+b x+c x^2} \tanh ^{-1}\left(\frac{b+2 c x}{2 \sqrt{c} \sqrt{a+b x+c x^2}}\right)}{128 c^{7/2} \sqrt{a x^2+b x^3+c x^4}}+\frac{x (b+6 c x) \sqrt{a x^2+b x^3+c x^4}}{24 c}",1,"-((5*b^2 - 12*a*c)*Sqrt[a*x^2 + b*x^3 + c*x^4])/(96*c^2) + (b*(15*b^2 - 52*a*c)*Sqrt[a*x^2 + b*x^3 + c*x^4])/(192*c^3*x) + (x*(b + 6*c*x)*Sqrt[a*x^2 + b*x^3 + c*x^4])/(24*c) - ((b^2 - 4*a*c)*(5*b^2 - 4*a*c)*x*Sqrt[a + b*x + c*x^2]*ArcTanh[(b + 2*c*x)/(2*Sqrt[c]*Sqrt[a + b*x + c*x^2])])/(128*c^(7/2)*Sqrt[a*x^2 + b*x^3 + c*x^4])","A",7,6,22,0.2727,1,"{1919, 1949, 12, 1914, 621, 206}"
31,1,163,0,0.0576031,"\int \sqrt{a x^2+b x^3+c x^4} \, dx","Int[Sqrt[a*x^2 + b*x^3 + c*x^4],x]","\frac{b \left(b^2-4 a c\right) \sqrt{a x^2+b x^3+c x^4} \tanh ^{-1}\left(\frac{b+2 c x}{2 \sqrt{c} \sqrt{a+b x+c x^2}}\right)}{16 c^{5/2} x \sqrt{a+b x+c x^2}}-\frac{b (b+2 c x) \sqrt{a x^2+b x^3+c x^4}}{8 c^2 x}+\frac{\left(a+b x+c x^2\right) \sqrt{a x^2+b x^3+c x^4}}{3 c x}","\frac{b \left(b^2-4 a c\right) \sqrt{a x^2+b x^3+c x^4} \tanh ^{-1}\left(\frac{b+2 c x}{2 \sqrt{c} \sqrt{a+b x+c x^2}}\right)}{16 c^{5/2} x \sqrt{a+b x+c x^2}}-\frac{b (b+2 c x) \sqrt{a x^2+b x^3+c x^4}}{8 c^2 x}+\frac{\left(a+b x+c x^2\right) \sqrt{a x^2+b x^3+c x^4}}{3 c x}",1,"-(b*(b + 2*c*x)*Sqrt[a*x^2 + b*x^3 + c*x^4])/(8*c^2*x) + ((a + b*x + c*x^2)*Sqrt[a*x^2 + b*x^3 + c*x^4])/(3*c*x) + (b*(b^2 - 4*a*c)*Sqrt[a*x^2 + b*x^3 + c*x^4]*ArcTanh[(b + 2*c*x)/(2*Sqrt[c]*Sqrt[a + b*x + c*x^2])])/(16*c^(5/2)*x*Sqrt[a + b*x + c*x^2])","A",5,5,20,0.2500,1,"{1903, 640, 612, 621, 206}"
32,1,119,0,0.0777735,"\int \frac{\sqrt{a x^2+b x^3+c x^4}}{x} \, dx","Int[Sqrt[a*x^2 + b*x^3 + c*x^4]/x,x]","\frac{(b+2 c x) \sqrt{a x^2+b x^3+c x^4}}{4 c x}-\frac{x \left(b^2-4 a c\right) \sqrt{a+b x+c x^2} \tanh ^{-1}\left(\frac{b+2 c x}{2 \sqrt{c} \sqrt{a+b x+c x^2}}\right)}{8 c^{3/2} \sqrt{a x^2+b x^3+c x^4}}","\frac{(b+2 c x) \sqrt{a x^2+b x^3+c x^4}}{4 c x}-\frac{x \left(b^2-4 a c\right) \sqrt{a+b x+c x^2} \tanh ^{-1}\left(\frac{b+2 c x}{2 \sqrt{c} \sqrt{a+b x+c x^2}}\right)}{8 c^{3/2} \sqrt{a x^2+b x^3+c x^4}}",1,"((b + 2*c*x)*Sqrt[a*x^2 + b*x^3 + c*x^4])/(4*c*x) - ((b^2 - 4*a*c)*x*Sqrt[a + b*x + c*x^2]*ArcTanh[(b + 2*c*x)/(2*Sqrt[c]*Sqrt[a + b*x + c*x^2])])/(8*c^(3/2)*Sqrt[a*x^2 + b*x^3 + c*x^4])","A",4,4,24,0.1667,1,"{1918, 1914, 621, 206}"
33,1,173,0,0.126323,"\int \frac{\sqrt{a x^2+b x^3+c x^4}}{x^2} \, dx","Int[Sqrt[a*x^2 + b*x^3 + c*x^4]/x^2,x]","\frac{\sqrt{a x^2+b x^3+c x^4}}{x}-\frac{\sqrt{a} x \sqrt{a+b x+c x^2} \tanh ^{-1}\left(\frac{2 a+b x}{2 \sqrt{a} \sqrt{a+b x+c x^2}}\right)}{\sqrt{a x^2+b x^3+c x^4}}+\frac{b x \sqrt{a+b x+c x^2} \tanh ^{-1}\left(\frac{b+2 c x}{2 \sqrt{c} \sqrt{a+b x+c x^2}}\right)}{2 \sqrt{c} \sqrt{a x^2+b x^3+c x^4}}","\frac{\sqrt{a x^2+b x^3+c x^4}}{x}-\frac{\sqrt{a} x \sqrt{a+b x+c x^2} \tanh ^{-1}\left(\frac{2 a+b x}{2 \sqrt{a} \sqrt{a+b x+c x^2}}\right)}{\sqrt{a x^2+b x^3+c x^4}}+\frac{b x \sqrt{a+b x+c x^2} \tanh ^{-1}\left(\frac{b+2 c x}{2 \sqrt{c} \sqrt{a+b x+c x^2}}\right)}{2 \sqrt{c} \sqrt{a x^2+b x^3+c x^4}}",1,"Sqrt[a*x^2 + b*x^3 + c*x^4]/x - (Sqrt[a]*x*Sqrt[a + b*x + c*x^2]*ArcTanh[(2*a + b*x)/(2*Sqrt[a]*Sqrt[a + b*x + c*x^2])])/Sqrt[a*x^2 + b*x^3 + c*x^4] + (b*x*Sqrt[a + b*x + c*x^2]*ArcTanh[(b + 2*c*x)/(2*Sqrt[c]*Sqrt[a + b*x + c*x^2])])/(2*Sqrt[c]*Sqrt[a*x^2 + b*x^3 + c*x^4])","A",7,6,24,0.2500,1,"{1921, 1933, 843, 621, 206, 724}"
34,1,173,0,0.1240737,"\int \frac{\sqrt{a x^2+b x^3+c x^4}}{x^3} \, dx","Int[Sqrt[a*x^2 + b*x^3 + c*x^4]/x^3,x]","-\frac{\sqrt{a x^2+b x^3+c x^4}}{x^2}-\frac{b x \sqrt{a+b x+c x^2} \tanh ^{-1}\left(\frac{2 a+b x}{2 \sqrt{a} \sqrt{a+b x+c x^2}}\right)}{2 \sqrt{a} \sqrt{a x^2+b x^3+c x^4}}+\frac{\sqrt{c} x \sqrt{a+b x+c x^2} \tanh ^{-1}\left(\frac{b+2 c x}{2 \sqrt{c} \sqrt{a+b x+c x^2}}\right)}{\sqrt{a x^2+b x^3+c x^4}}","-\frac{\sqrt{a x^2+b x^3+c x^4}}{x^2}-\frac{b x \sqrt{a+b x+c x^2} \tanh ^{-1}\left(\frac{2 a+b x}{2 \sqrt{a} \sqrt{a+b x+c x^2}}\right)}{2 \sqrt{a} \sqrt{a x^2+b x^3+c x^4}}+\frac{\sqrt{c} x \sqrt{a+b x+c x^2} \tanh ^{-1}\left(\frac{b+2 c x}{2 \sqrt{c} \sqrt{a+b x+c x^2}}\right)}{\sqrt{a x^2+b x^3+c x^4}}",1,"-(Sqrt[a*x^2 + b*x^3 + c*x^4]/x^2) - (b*x*Sqrt[a + b*x + c*x^2]*ArcTanh[(2*a + b*x)/(2*Sqrt[a]*Sqrt[a + b*x + c*x^2])])/(2*Sqrt[a]*Sqrt[a*x^2 + b*x^3 + c*x^4]) + (Sqrt[c]*x*Sqrt[a + b*x + c*x^2]*ArcTanh[(b + 2*c*x)/(2*Sqrt[c]*Sqrt[a + b*x + c*x^2])])/Sqrt[a*x^2 + b*x^3 + c*x^4]","A",7,6,24,0.2500,1,"{1920, 1933, 843, 621, 206, 724}"
35,1,114,0,0.1477005,"\int \frac{\sqrt{a x^2+b x^3+c x^4}}{x^4} \, dx","Int[Sqrt[a*x^2 + b*x^3 + c*x^4]/x^4,x]","\frac{\left(b^2-4 a c\right) \tanh ^{-1}\left(\frac{x (2 a+b x)}{2 \sqrt{a} \sqrt{a x^2+b x^3+c x^4}}\right)}{8 a^{3/2}}-\frac{b \sqrt{a x^2+b x^3+c x^4}}{4 a x^2}-\frac{\sqrt{a x^2+b x^3+c x^4}}{2 x^3}","\frac{\left(b^2-4 a c\right) \tanh ^{-1}\left(\frac{x (2 a+b x)}{2 \sqrt{a} \sqrt{a x^2+b x^3+c x^4}}\right)}{8 a^{3/2}}-\frac{b \sqrt{a x^2+b x^3+c x^4}}{4 a x^2}-\frac{\sqrt{a x^2+b x^3+c x^4}}{2 x^3}",1,"-Sqrt[a*x^2 + b*x^3 + c*x^4]/(2*x^3) - (b*Sqrt[a*x^2 + b*x^3 + c*x^4])/(4*a*x^2) + ((b^2 - 4*a*c)*ArcTanh[(x*(2*a + b*x))/(2*Sqrt[a]*Sqrt[a*x^2 + b*x^3 + c*x^4])])/(8*a^(3/2))","A",5,5,24,0.2083,1,"{1920, 1951, 12, 1904, 206}"
36,1,155,0,0.2558381,"\int \frac{\sqrt{a x^2+b x^3+c x^4}}{x^5} \, dx","Int[Sqrt[a*x^2 + b*x^3 + c*x^4]/x^5,x]","\frac{\left(3 b^2-8 a c\right) \sqrt{a x^2+b x^3+c x^4}}{24 a^2 x^2}-\frac{b \left(b^2-4 a c\right) \tanh ^{-1}\left(\frac{x (2 a+b x)}{2 \sqrt{a} \sqrt{a x^2+b x^3+c x^4}}\right)}{16 a^{5/2}}-\frac{b \sqrt{a x^2+b x^3+c x^4}}{12 a x^3}-\frac{\sqrt{a x^2+b x^3+c x^4}}{3 x^4}","\frac{\left(3 b^2-8 a c\right) \sqrt{a x^2+b x^3+c x^4}}{24 a^2 x^2}-\frac{b \left(b^2-4 a c\right) \tanh ^{-1}\left(\frac{x (2 a+b x)}{2 \sqrt{a} \sqrt{a x^2+b x^3+c x^4}}\right)}{16 a^{5/2}}-\frac{b \sqrt{a x^2+b x^3+c x^4}}{12 a x^3}-\frac{\sqrt{a x^2+b x^3+c x^4}}{3 x^4}",1,"-Sqrt[a*x^2 + b*x^3 + c*x^4]/(3*x^4) - (b*Sqrt[a*x^2 + b*x^3 + c*x^4])/(12*a*x^3) + ((3*b^2 - 8*a*c)*Sqrt[a*x^2 + b*x^3 + c*x^4])/(24*a^2*x^2) - (b*(b^2 - 4*a*c)*ArcTanh[(x*(2*a + b*x))/(2*Sqrt[a]*Sqrt[a*x^2 + b*x^3 + c*x^4])])/(16*a^(5/2))","A",6,5,24,0.2083,1,"{1920, 1951, 12, 1904, 206}"
37,1,205,0,0.3858477,"\int \frac{\sqrt{a x^2+b x^3+c x^4}}{x^6} \, dx","Int[Sqrt[a*x^2 + b*x^3 + c*x^4]/x^6,x]","-\frac{b \left(15 b^2-52 a c\right) \sqrt{a x^2+b x^3+c x^4}}{192 a^3 x^2}+\frac{\left(5 b^2-12 a c\right) \sqrt{a x^2+b x^3+c x^4}}{96 a^2 x^3}+\frac{\left(b^2-4 a c\right) \left(5 b^2-4 a c\right) \tanh ^{-1}\left(\frac{x (2 a+b x)}{2 \sqrt{a} \sqrt{a x^2+b x^3+c x^4}}\right)}{128 a^{7/2}}-\frac{b \sqrt{a x^2+b x^3+c x^4}}{24 a x^4}-\frac{\sqrt{a x^2+b x^3+c x^4}}{4 x^5}","-\frac{b \left(15 b^2-52 a c\right) \sqrt{a x^2+b x^3+c x^4}}{192 a^3 x^2}+\frac{\left(5 b^2-12 a c\right) \sqrt{a x^2+b x^3+c x^4}}{96 a^2 x^3}+\frac{\left(b^2-4 a c\right) \left(5 b^2-4 a c\right) \tanh ^{-1}\left(\frac{x (2 a+b x)}{2 \sqrt{a} \sqrt{a x^2+b x^3+c x^4}}\right)}{128 a^{7/2}}-\frac{b \sqrt{a x^2+b x^3+c x^4}}{24 a x^4}-\frac{\sqrt{a x^2+b x^3+c x^4}}{4 x^5}",1,"-Sqrt[a*x^2 + b*x^3 + c*x^4]/(4*x^5) - (b*Sqrt[a*x^2 + b*x^3 + c*x^4])/(24*a*x^4) + ((5*b^2 - 12*a*c)*Sqrt[a*x^2 + b*x^3 + c*x^4])/(96*a^2*x^3) - (b*(15*b^2 - 52*a*c)*Sqrt[a*x^2 + b*x^3 + c*x^4])/(192*a^3*x^2) + ((b^2 - 4*a*c)*(5*b^2 - 4*a*c)*ArcTanh[(x*(2*a + b*x))/(2*Sqrt[a]*Sqrt[a*x^2 + b*x^3 + c*x^4])])/(128*a^(7/2))","A",7,5,24,0.2083,1,"{1920, 1951, 12, 1904, 206}"
38,1,422,0,1.2033906,"\int x \left(a x^2+b x^3+c x^4\right)^{3/2} \, dx","Int[x*(a*x^2 + b*x^3 + c*x^4)^(3/2),x]","\frac{x^2 \left(560 a^2 c^2-568 a b^2 c+99 b^4\right) \sqrt{a x^2+b x^3+c x^4}}{35840 c^3}-\frac{b x \left(2416 a^2 c^2-1560 a b^2 c+231 b^4\right) \sqrt{a x^2+b x^3+c x^4}}{71680 c^4}+\frac{\left(18896 a^2 b^2 c^2-6720 a^3 c^3-8988 a b^4 c+1155 b^6\right) \sqrt{a x^2+b x^3+c x^4}}{286720 c^5}-\frac{b \left(81648 a^2 b^2 c^2-58816 a^3 c^3-30660 a b^4 c+3465 b^6\right) \sqrt{a x^2+b x^3+c x^4}}{573440 c^6 x}+\frac{3 x \left(b^2-4 a c\right)^2 \left(16 a^2 c^2-72 a b^2 c+33 b^4\right) \sqrt{a+b x+c x^2} \tanh ^{-1}\left(\frac{b+2 c x}{2 \sqrt{c} \sqrt{a+b x+c x^2}}\right)}{32768 c^{13/2} \sqrt{a x^2+b x^3+c x^4}}-\frac{x^3 \left(10 c x \left(11 b^2-28 a c\right)+b \left(68 a c+11 b^2\right)\right) \sqrt{a x^2+b x^3+c x^4}}{4480 c^2}+\frac{x (3 b+14 c x) \left(a x^2+b x^3+c x^4\right)^{3/2}}{112 c}","\frac{x^2 \left(560 a^2 c^2-568 a b^2 c+99 b^4\right) \sqrt{a x^2+b x^3+c x^4}}{35840 c^3}-\frac{b x \left(2416 a^2 c^2-1560 a b^2 c+231 b^4\right) \sqrt{a x^2+b x^3+c x^4}}{71680 c^4}+\frac{\left(18896 a^2 b^2 c^2-6720 a^3 c^3-8988 a b^4 c+1155 b^6\right) \sqrt{a x^2+b x^3+c x^4}}{286720 c^5}-\frac{b \left(81648 a^2 b^2 c^2-58816 a^3 c^3-30660 a b^4 c+3465 b^6\right) \sqrt{a x^2+b x^3+c x^4}}{573440 c^6 x}+\frac{3 x \left(b^2-4 a c\right)^2 \left(16 a^2 c^2-72 a b^2 c+33 b^4\right) \sqrt{a+b x+c x^2} \tanh ^{-1}\left(\frac{b+2 c x}{2 \sqrt{c} \sqrt{a+b x+c x^2}}\right)}{32768 c^{13/2} \sqrt{a x^2+b x^3+c x^4}}-\frac{x^3 \left(10 c x \left(11 b^2-28 a c\right)+b \left(68 a c+11 b^2\right)\right) \sqrt{a x^2+b x^3+c x^4}}{4480 c^2}+\frac{x (3 b+14 c x) \left(a x^2+b x^3+c x^4\right)^{3/2}}{112 c}",1,"((1155*b^6 - 8988*a*b^4*c + 18896*a^2*b^2*c^2 - 6720*a^3*c^3)*Sqrt[a*x^2 + b*x^3 + c*x^4])/(286720*c^5) - (b*(3465*b^6 - 30660*a*b^4*c + 81648*a^2*b^2*c^2 - 58816*a^3*c^3)*Sqrt[a*x^2 + b*x^3 + c*x^4])/(573440*c^6*x) - (b*(231*b^4 - 1560*a*b^2*c + 2416*a^2*c^2)*x*Sqrt[a*x^2 + b*x^3 + c*x^4])/(71680*c^4) + ((99*b^4 - 568*a*b^2*c + 560*a^2*c^2)*x^2*Sqrt[a*x^2 + b*x^3 + c*x^4])/(35840*c^3) - (x^3*(b*(11*b^2 + 68*a*c) + 10*c*(11*b^2 - 28*a*c)*x)*Sqrt[a*x^2 + b*x^3 + c*x^4])/(4480*c^2) + (x*(3*b + 14*c*x)*(a*x^2 + b*x^3 + c*x^4)^(3/2))/(112*c) + (3*(b^2 - 4*a*c)^2*(33*b^4 - 72*a*b^2*c + 16*a^2*c^2)*x*Sqrt[a + b*x + c*x^2]*ArcTanh[(b + 2*c*x)/(2*Sqrt[c]*Sqrt[a + b*x + c*x^2])])/(32768*c^(13/2)*Sqrt[a*x^2 + b*x^3 + c*x^4])","A",10,7,22,0.3182,1,"{1919, 1945, 1949, 12, 1914, 621, 206}"
39,1,364,0,1.0394309,"\int \left(a x^2+b x^3+c x^4\right)^{3/2} \, dx","Int[(a*x^2 + b*x^3 + c*x^4)^(3/2),x]","-\frac{b \left(1168 a^2 c^2-728 a b^2 c+105 b^4\right) \sqrt{a x^2+b x^3+c x^4}}{17920 c^4}+\frac{\left(5488 a^2 b^2 c^2-2048 a^3 c^3-2520 a b^4 c+315 b^6\right) \sqrt{a x^2+b x^3+c x^4}}{35840 c^5 x}-\frac{b x^2 \left(9 b^2-44 a c\right) \sqrt{a x^2+b x^3+c x^4}}{2240 c^2}+\frac{x \left(7 b^2-32 a c\right) \left(3 b^2-4 a c\right) \sqrt{a x^2+b x^3+c x^4}}{4480 c^3}-\frac{3 b x \left(b^2-4 a c\right)^2 \left(3 b^2-4 a c\right) \sqrt{a+b x+c x^2} \tanh ^{-1}\left(\frac{b+2 c x}{2 \sqrt{c} \sqrt{a+b x+c x^2}}\right)}{2048 c^{11/2} \sqrt{a x^2+b x^3+c x^4}}+\frac{x^3 \left(24 a c+b^2+10 b c x\right) \sqrt{a x^2+b x^3+c x^4}}{280 c}+\frac{1}{7} x \left(a x^2+b x^3+c x^4\right)^{3/2}","-\frac{b \left(1168 a^2 c^2-728 a b^2 c+105 b^4\right) \sqrt{a x^2+b x^3+c x^4}}{17920 c^4}+\frac{\left(5488 a^2 b^2 c^2-2048 a^3 c^3-2520 a b^4 c+315 b^6\right) \sqrt{a x^2+b x^3+c x^4}}{35840 c^5 x}-\frac{b x^2 \left(9 b^2-44 a c\right) \sqrt{a x^2+b x^3+c x^4}}{2240 c^2}+\frac{x \left(7 b^2-32 a c\right) \left(3 b^2-4 a c\right) \sqrt{a x^2+b x^3+c x^4}}{4480 c^3}-\frac{3 b x \left(b^2-4 a c\right)^2 \left(3 b^2-4 a c\right) \sqrt{a+b x+c x^2} \tanh ^{-1}\left(\frac{b+2 c x}{2 \sqrt{c} \sqrt{a+b x+c x^2}}\right)}{2048 c^{11/2} \sqrt{a x^2+b x^3+c x^4}}+\frac{x^3 \left(24 a c+b^2+10 b c x\right) \sqrt{a x^2+b x^3+c x^4}}{280 c}+\frac{1}{7} x \left(a x^2+b x^3+c x^4\right)^{3/2}",1,"-(b*(105*b^4 - 728*a*b^2*c + 1168*a^2*c^2)*Sqrt[a*x^2 + b*x^3 + c*x^4])/(17920*c^4) + ((315*b^6 - 2520*a*b^4*c + 5488*a^2*b^2*c^2 - 2048*a^3*c^3)*Sqrt[a*x^2 + b*x^3 + c*x^4])/(35840*c^5*x) + ((7*b^2 - 32*a*c)*(3*b^2 - 4*a*c)*x*Sqrt[a*x^2 + b*x^3 + c*x^4])/(4480*c^3) - (b*(9*b^2 - 44*a*c)*x^2*Sqrt[a*x^2 + b*x^3 + c*x^4])/(2240*c^2) + (x^3*(b^2 + 24*a*c + 10*b*c*x)*Sqrt[a*x^2 + b*x^3 + c*x^4])/(280*c) + (x*(a*x^2 + b*x^3 + c*x^4)^(3/2))/7 - (3*b*(b^2 - 4*a*c)^2*(3*b^2 - 4*a*c)*x*Sqrt[a + b*x + c*x^2]*ArcTanh[(b + 2*c*x)/(2*Sqrt[c]*Sqrt[a + b*x + c*x^2])])/(2048*c^(11/2)*Sqrt[a*x^2 + b*x^3 + c*x^4])","A",10,7,20,0.3500,1,"{1906, 1945, 1949, 12, 1914, 621, 206}"
40,1,288,0,0.5192348,"\int \frac{\left(a x^2+b x^3+c x^4\right)^{3/2}}{x} \, dx","Int[(a*x^2 + b*x^3 + c*x^4)^(3/2)/x,x]","\frac{\left(240 a^2 c^2-216 a b^2 c+35 b^4\right) \sqrt{a x^2+b x^3+c x^4}}{3840 c^3}-\frac{b \left(1296 a^2 c^2-760 a b^2 c+105 b^4\right) \sqrt{a x^2+b x^3+c x^4}}{7680 c^4 x}-\frac{x \left(6 c x \left(7 b^2-20 a c\right)+b \left(12 a c+7 b^2\right)\right) \sqrt{a x^2+b x^3+c x^4}}{960 c^2}+\frac{x \left(7 b^2-4 a c\right) \left(b^2-4 a c\right)^2 \sqrt{a+b x+c x^2} \tanh ^{-1}\left(\frac{b+2 c x}{2 \sqrt{c} \sqrt{a+b x+c x^2}}\right)}{1024 c^{9/2} \sqrt{a x^2+b x^3+c x^4}}+\frac{(3 b+10 c x) \left(a x^2+b x^3+c x^4\right)^{3/2}}{60 c x}","\frac{\left(240 a^2 c^2-216 a b^2 c+35 b^4\right) \sqrt{a x^2+b x^3+c x^4}}{3840 c^3}-\frac{b \left(1296 a^2 c^2-760 a b^2 c+105 b^4\right) \sqrt{a x^2+b x^3+c x^4}}{7680 c^4 x}-\frac{x \left(6 c x \left(7 b^2-20 a c\right)+b \left(12 a c+7 b^2\right)\right) \sqrt{a x^2+b x^3+c x^4}}{960 c^2}+\frac{x \left(7 b^2-4 a c\right) \left(b^2-4 a c\right)^2 \sqrt{a+b x+c x^2} \tanh ^{-1}\left(\frac{b+2 c x}{2 \sqrt{c} \sqrt{a+b x+c x^2}}\right)}{1024 c^{9/2} \sqrt{a x^2+b x^3+c x^4}}+\frac{(3 b+10 c x) \left(a x^2+b x^3+c x^4\right)^{3/2}}{60 c x}",1,"((35*b^4 - 216*a*b^2*c + 240*a^2*c^2)*Sqrt[a*x^2 + b*x^3 + c*x^4])/(3840*c^3) - (b*(105*b^4 - 760*a*b^2*c + 1296*a^2*c^2)*Sqrt[a*x^2 + b*x^3 + c*x^4])/(7680*c^4*x) - (x*(b*(7*b^2 + 12*a*c) + 6*c*(7*b^2 - 20*a*c)*x)*Sqrt[a*x^2 + b*x^3 + c*x^4])/(960*c^2) + ((3*b + 10*c*x)*(a*x^2 + b*x^3 + c*x^4)^(3/2))/(60*c*x) + ((b^2 - 4*a*c)^2*(7*b^2 - 4*a*c)*x*Sqrt[a + b*x + c*x^2]*ArcTanh[(b + 2*c*x)/(2*Sqrt[c]*Sqrt[a + b*x + c*x^2])])/(1024*c^(9/2)*Sqrt[a*x^2 + b*x^3 + c*x^4])","A",8,7,24,0.2917,1,"{1919, 1934, 1949, 12, 1914, 621, 206}"
41,1,198,0,0.1781016,"\int \frac{\left(a x^2+b x^3+c x^4\right)^{3/2}}{x^2} \, dx","Int[(a*x^2 + b*x^3 + c*x^4)^(3/2)/x^2,x]","\frac{3 b \left(b^2-4 a c\right) (b+2 c x) \sqrt{a x^2+b x^3+c x^4}}{128 c^3 x}-\frac{3 b x \left(b^2-4 a c\right)^2 \sqrt{a+b x+c x^2} \tanh ^{-1}\left(\frac{b+2 c x}{2 \sqrt{c} \sqrt{a+b x+c x^2}}\right)}{256 c^{7/2} \sqrt{a x^2+b x^3+c x^4}}-\frac{b (b+2 c x) \left(a x^2+b x^3+c x^4\right)^{3/2}}{16 c^2 x^3}+\frac{\left(a x^2+b x^3+c x^4\right)^{5/2}}{5 c x^5}","\frac{3 b \left(b^2-4 a c\right) (b+2 c x) \sqrt{a x^2+b x^3+c x^4}}{128 c^3 x}-\frac{3 b x \left(b^2-4 a c\right)^2 \sqrt{a+b x+c x^2} \tanh ^{-1}\left(\frac{b+2 c x}{2 \sqrt{c} \sqrt{a+b x+c x^2}}\right)}{256 c^{7/2} \sqrt{a x^2+b x^3+c x^4}}-\frac{b (b+2 c x) \left(a x^2+b x^3+c x^4\right)^{3/2}}{16 c^2 x^3}+\frac{\left(a x^2+b x^3+c x^4\right)^{5/2}}{5 c x^5}",1,"(3*b*(b^2 - 4*a*c)*(b + 2*c*x)*Sqrt[a*x^2 + b*x^3 + c*x^4])/(128*c^3*x) - (b*(b + 2*c*x)*(a*x^2 + b*x^3 + c*x^4)^(3/2))/(16*c^2*x^3) + (a*x^2 + b*x^3 + c*x^4)^(5/2)/(5*c*x^5) - (3*b*(b^2 - 4*a*c)^2*x*Sqrt[a + b*x + c*x^2]*ArcTanh[(b + 2*c*x)/(2*Sqrt[c]*Sqrt[a + b*x + c*x^2])])/(256*c^(7/2)*Sqrt[a*x^2 + b*x^3 + c*x^4])","A",6,5,24,0.2083,1,"{1917, 1918, 1914, 621, 206}"
42,1,165,0,0.1277575,"\int \frac{\left(a x^2+b x^3+c x^4\right)^{3/2}}{x^3} \, dx","Int[(a*x^2 + b*x^3 + c*x^4)^(3/2)/x^3,x]","-\frac{3 \left(b^2-4 a c\right) (b+2 c x) \sqrt{a x^2+b x^3+c x^4}}{64 c^2 x}+\frac{3 x \left(b^2-4 a c\right)^2 \sqrt{a+b x+c x^2} \tanh ^{-1}\left(\frac{b+2 c x}{2 \sqrt{c} \sqrt{a+b x+c x^2}}\right)}{128 c^{5/2} \sqrt{a x^2+b x^3+c x^4}}+\frac{(b+2 c x) \left(a x^2+b x^3+c x^4\right)^{3/2}}{8 c x^3}","-\frac{3 \left(b^2-4 a c\right) (b+2 c x) \sqrt{a x^2+b x^3+c x^4}}{64 c^2 x}+\frac{3 x \left(b^2-4 a c\right)^2 \sqrt{a+b x+c x^2} \tanh ^{-1}\left(\frac{b+2 c x}{2 \sqrt{c} \sqrt{a+b x+c x^2}}\right)}{128 c^{5/2} \sqrt{a x^2+b x^3+c x^4}}+\frac{(b+2 c x) \left(a x^2+b x^3+c x^4\right)^{3/2}}{8 c x^3}",1,"(-3*(b^2 - 4*a*c)*(b + 2*c*x)*Sqrt[a*x^2 + b*x^3 + c*x^4])/(64*c^2*x) + ((b + 2*c*x)*(a*x^2 + b*x^3 + c*x^4)^(3/2))/(8*c*x^3) + (3*(b^2 - 4*a*c)^2*x*Sqrt[a + b*x + c*x^2]*ArcTanh[(b + 2*c*x)/(2*Sqrt[c]*Sqrt[a + b*x + c*x^2])])/(128*c^(5/2)*Sqrt[a*x^2 + b*x^3 + c*x^4])","A",5,4,24,0.1667,1,"{1918, 1914, 621, 206}"
43,1,227,0,0.2552945,"\int \frac{\left(a x^2+b x^3+c x^4\right)^{3/2}}{x^4} \, dx","Int[(a*x^2 + b*x^3 + c*x^4)^(3/2)/x^4,x]","-\frac{a^{3/2} x \sqrt{a+b x+c x^2} \tanh ^{-1}\left(\frac{2 a+b x}{2 \sqrt{a} \sqrt{a+b x+c x^2}}\right)}{\sqrt{a x^2+b x^3+c x^4}}-\frac{b x \left(b^2-12 a c\right) \sqrt{a+b x+c x^2} \tanh ^{-1}\left(\frac{b+2 c x}{2 \sqrt{c} \sqrt{a+b x+c x^2}}\right)}{16 c^{3/2} \sqrt{a x^2+b x^3+c x^4}}+\frac{\left(8 a c+b^2+2 b c x\right) \sqrt{a x^2+b x^3+c x^4}}{8 c x}+\frac{\left(a x^2+b x^3+c x^4\right)^{3/2}}{3 x^3}","-\frac{a^{3/2} x \sqrt{a+b x+c x^2} \tanh ^{-1}\left(\frac{2 a+b x}{2 \sqrt{a} \sqrt{a+b x+c x^2}}\right)}{\sqrt{a x^2+b x^3+c x^4}}-\frac{b x \left(b^2-12 a c\right) \sqrt{a+b x+c x^2} \tanh ^{-1}\left(\frac{b+2 c x}{2 \sqrt{c} \sqrt{a+b x+c x^2}}\right)}{16 c^{3/2} \sqrt{a x^2+b x^3+c x^4}}+\frac{\left(8 a c+b^2+2 b c x\right) \sqrt{a x^2+b x^3+c x^4}}{8 c x}+\frac{\left(a x^2+b x^3+c x^4\right)^{3/2}}{3 x^3}",1,"((b^2 + 8*a*c + 2*b*c*x)*Sqrt[a*x^2 + b*x^3 + c*x^4])/(8*c*x) + (a*x^2 + b*x^3 + c*x^4)^(3/2)/(3*x^3) - (a^(3/2)*x*Sqrt[a + b*x + c*x^2]*ArcTanh[(2*a + b*x)/(2*Sqrt[a]*Sqrt[a + b*x + c*x^2])])/Sqrt[a*x^2 + b*x^3 + c*x^4] - (b*(b^2 - 12*a*c)*x*Sqrt[a + b*x + c*x^2]*ArcTanh[(b + 2*c*x)/(2*Sqrt[c]*Sqrt[a + b*x + c*x^2])])/(16*c^(3/2)*Sqrt[a*x^2 + b*x^3 + c*x^4])","A",8,7,24,0.2917,1,"{1921, 1945, 1933, 843, 621, 206, 724}"
44,1,219,0,0.2420144,"\int \frac{\left(a x^2+b x^3+c x^4\right)^{3/2}}{x^5} \, dx","Int[(a*x^2 + b*x^3 + c*x^4)^(3/2)/x^5,x]","\frac{3 x \left(4 a c+b^2\right) \sqrt{a+b x+c x^2} \tanh ^{-1}\left(\frac{b+2 c x}{2 \sqrt{c} \sqrt{a+b x+c x^2}}\right)}{8 \sqrt{c} \sqrt{a x^2+b x^3+c x^4}}-\frac{\left(a x^2+b x^3+c x^4\right)^{3/2}}{x^4}+\frac{3 (3 b+2 c x) \sqrt{a x^2+b x^3+c x^4}}{4 x}-\frac{3 \sqrt{a} b x \sqrt{a+b x+c x^2} \tanh ^{-1}\left(\frac{2 a+b x}{2 \sqrt{a} \sqrt{a+b x+c x^2}}\right)}{2 \sqrt{a x^2+b x^3+c x^4}}","\frac{3 x \left(4 a c+b^2\right) \sqrt{a+b x+c x^2} \tanh ^{-1}\left(\frac{b+2 c x}{2 \sqrt{c} \sqrt{a+b x+c x^2}}\right)}{8 \sqrt{c} \sqrt{a x^2+b x^3+c x^4}}-\frac{\left(a x^2+b x^3+c x^4\right)^{3/2}}{x^4}+\frac{3 (3 b+2 c x) \sqrt{a x^2+b x^3+c x^4}}{4 x}-\frac{3 \sqrt{a} b x \sqrt{a+b x+c x^2} \tanh ^{-1}\left(\frac{2 a+b x}{2 \sqrt{a} \sqrt{a+b x+c x^2}}\right)}{2 \sqrt{a x^2+b x^3+c x^4}}",1,"(3*(3*b + 2*c*x)*Sqrt[a*x^2 + b*x^3 + c*x^4])/(4*x) - (a*x^2 + b*x^3 + c*x^4)^(3/2)/x^4 - (3*Sqrt[a]*b*x*Sqrt[a + b*x + c*x^2]*ArcTanh[(2*a + b*x)/(2*Sqrt[a]*Sqrt[a + b*x + c*x^2])])/(2*Sqrt[a*x^2 + b*x^3 + c*x^4]) + (3*(b^2 + 4*a*c)*x*Sqrt[a + b*x + c*x^2]*ArcTanh[(b + 2*c*x)/(2*Sqrt[c]*Sqrt[a + b*x + c*x^2])])/(8*Sqrt[c]*Sqrt[a*x^2 + b*x^3 + c*x^4])","A",8,7,24,0.2917,1,"{1920, 1945, 1933, 843, 621, 206, 724}"
45,1,219,0,0.2377849,"\int \frac{\left(a x^2+b x^3+c x^4\right)^{3/2}}{x^6} \, dx","Int[(a*x^2 + b*x^3 + c*x^4)^(3/2)/x^6,x]","-\frac{3 x \left(4 a c+b^2\right) \sqrt{a+b x+c x^2} \tanh ^{-1}\left(\frac{2 a+b x}{2 \sqrt{a} \sqrt{a+b x+c x^2}}\right)}{8 \sqrt{a} \sqrt{a x^2+b x^3+c x^4}}-\frac{\left(a x^2+b x^3+c x^4\right)^{3/2}}{2 x^5}-\frac{3 (b-2 c x) \sqrt{a x^2+b x^3+c x^4}}{4 x^2}+\frac{3 b \sqrt{c} x \sqrt{a+b x+c x^2} \tanh ^{-1}\left(\frac{b+2 c x}{2 \sqrt{c} \sqrt{a+b x+c x^2}}\right)}{2 \sqrt{a x^2+b x^3+c x^4}}","-\frac{3 x \left(4 a c+b^2\right) \sqrt{a+b x+c x^2} \tanh ^{-1}\left(\frac{2 a+b x}{2 \sqrt{a} \sqrt{a+b x+c x^2}}\right)}{8 \sqrt{a} \sqrt{a x^2+b x^3+c x^4}}-\frac{\left(a x^2+b x^3+c x^4\right)^{3/2}}{2 x^5}-\frac{3 (b-2 c x) \sqrt{a x^2+b x^3+c x^4}}{4 x^2}+\frac{3 b \sqrt{c} x \sqrt{a+b x+c x^2} \tanh ^{-1}\left(\frac{b+2 c x}{2 \sqrt{c} \sqrt{a+b x+c x^2}}\right)}{2 \sqrt{a x^2+b x^3+c x^4}}",1,"(-3*(b - 2*c*x)*Sqrt[a*x^2 + b*x^3 + c*x^4])/(4*x^2) - (a*x^2 + b*x^3 + c*x^4)^(3/2)/(2*x^5) - (3*(b^2 + 4*a*c)*x*Sqrt[a + b*x + c*x^2]*ArcTanh[(2*a + b*x)/(2*Sqrt[a]*Sqrt[a + b*x + c*x^2])])/(8*Sqrt[a]*Sqrt[a*x^2 + b*x^3 + c*x^4]) + (3*b*Sqrt[c]*x*Sqrt[a + b*x + c*x^2]*ArcTanh[(b + 2*c*x)/(2*Sqrt[c]*Sqrt[a + b*x + c*x^2])])/(2*Sqrt[a*x^2 + b*x^3 + c*x^4])","A",8,7,24,0.2917,1,"{1920, 1941, 1933, 843, 621, 206, 724}"
46,1,257,0,0.3505638,"\int \frac{\left(a x^2+b x^3+c x^4\right)^{3/2}}{x^7} \, dx","Int[(a*x^2 + b*x^3 + c*x^4)^(3/2)/x^7,x]","\frac{b x \left(b^2-12 a c\right) \sqrt{a+b x+c x^2} \tanh ^{-1}\left(\frac{2 a+b x}{2 \sqrt{a} \sqrt{a+b x+c x^2}}\right)}{16 a^{3/2} \sqrt{a x^2+b x^3+c x^4}}+\frac{\left(-8 a c+b^2+2 b c x\right) \sqrt{a x^2+b x^3+c x^4}}{8 a x^2}+\frac{c^{3/2} x \sqrt{a+b x+c x^2} \tanh ^{-1}\left(\frac{b+2 c x}{2 \sqrt{c} \sqrt{a+b x+c x^2}}\right)}{\sqrt{a x^2+b x^3+c x^4}}-\frac{b \left(a x^2+b x^3+c x^4\right)^{3/2}}{4 a x^5}-\frac{\left(a x^2+b x^3+c x^4\right)^{3/2}}{3 x^6}","\frac{b x \left(b^2-12 a c\right) \sqrt{a+b x+c x^2} \tanh ^{-1}\left(\frac{2 a+b x}{2 \sqrt{a} \sqrt{a+b x+c x^2}}\right)}{16 a^{3/2} \sqrt{a x^2+b x^3+c x^4}}+\frac{\left(-8 a c+b^2+2 b c x\right) \sqrt{a x^2+b x^3+c x^4}}{8 a x^2}+\frac{c^{3/2} x \sqrt{a+b x+c x^2} \tanh ^{-1}\left(\frac{b+2 c x}{2 \sqrt{c} \sqrt{a+b x+c x^2}}\right)}{\sqrt{a x^2+b x^3+c x^4}}-\frac{b \left(a x^2+b x^3+c x^4\right)^{3/2}}{4 a x^5}-\frac{\left(a x^2+b x^3+c x^4\right)^{3/2}}{3 x^6}",1,"((b^2 - 8*a*c + 2*b*c*x)*Sqrt[a*x^2 + b*x^3 + c*x^4])/(8*a*x^2) - (a*x^2 + b*x^3 + c*x^4)^(3/2)/(3*x^6) - (b*(a*x^2 + b*x^3 + c*x^4)^(3/2))/(4*a*x^5) + (b*(b^2 - 12*a*c)*x*Sqrt[a + b*x + c*x^2]*ArcTanh[(2*a + b*x)/(2*Sqrt[a]*Sqrt[a + b*x + c*x^2])])/(16*a^(3/2)*Sqrt[a*x^2 + b*x^3 + c*x^4]) + (c^(3/2)*x*Sqrt[a + b*x + c*x^2]*ArcTanh[(b + 2*c*x)/(2*Sqrt[c]*Sqrt[a + b*x + c*x^2])])/Sqrt[a*x^2 + b*x^3 + c*x^4]","A",9,8,24,0.3333,1,"{1920, 1951, 1941, 1933, 843, 621, 206, 724}"
47,1,197,0,0.3628475,"\int \frac{\left(a x^2+b x^3+c x^4\right)^{3/2}}{x^8} \, dx","Int[(a*x^2 + b*x^3 + c*x^4)^(3/2)/x^8,x]","\frac{b \left(3 b^2-20 a c\right) \sqrt{a x^2+b x^3+c x^4}}{64 a^2 x^2}-\frac{3 \left(b^2-4 a c\right)^2 \tanh ^{-1}\left(\frac{x (2 a+b x)}{2 \sqrt{a} \sqrt{a x^2+b x^3+c x^4}}\right)}{128 a^{5/2}}-\frac{\left(b^2-12 a c\right) \sqrt{a x^2+b x^3+c x^4}}{32 a x^3}-\frac{\left(a x^2+b x^3+c x^4\right)^{3/2}}{4 x^7}-\frac{(b+6 c x) \sqrt{a x^2+b x^3+c x^4}}{8 x^4}","\frac{b \left(3 b^2-20 a c\right) \sqrt{a x^2+b x^3+c x^4}}{64 a^2 x^2}-\frac{3 \left(b^2-4 a c\right)^2 \tanh ^{-1}\left(\frac{x (2 a+b x)}{2 \sqrt{a} \sqrt{a x^2+b x^3+c x^4}}\right)}{128 a^{5/2}}-\frac{\left(b^2-12 a c\right) \sqrt{a x^2+b x^3+c x^4}}{32 a x^3}-\frac{\left(a x^2+b x^3+c x^4\right)^{3/2}}{4 x^7}-\frac{(b+6 c x) \sqrt{a x^2+b x^3+c x^4}}{8 x^4}",1,"-((b^2 - 12*a*c)*Sqrt[a*x^2 + b*x^3 + c*x^4])/(32*a*x^3) + (b*(3*b^2 - 20*a*c)*Sqrt[a*x^2 + b*x^3 + c*x^4])/(64*a^2*x^2) - ((b + 6*c*x)*Sqrt[a*x^2 + b*x^3 + c*x^4])/(8*x^4) - (a*x^2 + b*x^3 + c*x^4)^(3/2)/(4*x^7) - (3*(b^2 - 4*a*c)^2*ArcTanh[(x*(2*a + b*x))/(2*Sqrt[a]*Sqrt[a*x^2 + b*x^3 + c*x^4])])/(128*a^(5/2))","A",7,6,24,0.2500,1,"{1920, 1941, 1951, 12, 1904, 206}"
48,1,249,0,0.5038527,"\int \frac{\left(a x^2+b x^3+c x^4\right)^{3/2}}{x^9} \, dx","Int[(a*x^2 + b*x^3 + c*x^4)^(3/2)/x^9,x]","-\frac{\left(128 a^2 c^2-100 a b^2 c+15 b^4\right) \sqrt{a x^2+b x^3+c x^4}}{640 a^3 x^2}+\frac{b \left(5 b^2-28 a c\right) \sqrt{a x^2+b x^3+c x^4}}{320 a^2 x^3}+\frac{3 b \left(b^2-4 a c\right)^2 \tanh ^{-1}\left(\frac{x (2 a+b x)}{2 \sqrt{a} \sqrt{a x^2+b x^3+c x^4}}\right)}{256 a^{7/2}}-\frac{\left(b^2-8 a c\right) \sqrt{a x^2+b x^3+c x^4}}{80 a x^4}-\frac{\left(a x^2+b x^3+c x^4\right)^{3/2}}{5 x^8}-\frac{3 (b+4 c x) \sqrt{a x^2+b x^3+c x^4}}{40 x^5}","-\frac{\left(128 a^2 c^2-100 a b^2 c+15 b^4\right) \sqrt{a x^2+b x^3+c x^4}}{640 a^3 x^2}+\frac{b \left(5 b^2-28 a c\right) \sqrt{a x^2+b x^3+c x^4}}{320 a^2 x^3}+\frac{3 b \left(b^2-4 a c\right)^2 \tanh ^{-1}\left(\frac{x (2 a+b x)}{2 \sqrt{a} \sqrt{a x^2+b x^3+c x^4}}\right)}{256 a^{7/2}}-\frac{\left(b^2-8 a c\right) \sqrt{a x^2+b x^3+c x^4}}{80 a x^4}-\frac{\left(a x^2+b x^3+c x^4\right)^{3/2}}{5 x^8}-\frac{3 (b+4 c x) \sqrt{a x^2+b x^3+c x^4}}{40 x^5}",1,"-((b^2 - 8*a*c)*Sqrt[a*x^2 + b*x^3 + c*x^4])/(80*a*x^4) + (b*(5*b^2 - 28*a*c)*Sqrt[a*x^2 + b*x^3 + c*x^4])/(320*a^2*x^3) - ((15*b^4 - 100*a*b^2*c + 128*a^2*c^2)*Sqrt[a*x^2 + b*x^3 + c*x^4])/(640*a^3*x^2) - (3*(b + 4*c*x)*Sqrt[a*x^2 + b*x^3 + c*x^4])/(40*x^5) - (a*x^2 + b*x^3 + c*x^4)^(3/2)/(5*x^8) + (3*b*(b^2 - 4*a*c)^2*ArcTanh[(x*(2*a + b*x))/(2*Sqrt[a]*Sqrt[a*x^2 + b*x^3 + c*x^4])])/(256*a^(7/2))","A",8,6,24,0.2500,1,"{1920, 1941, 1951, 12, 1904, 206}"
49,1,143,0,0.1740071,"\int \frac{x^3}{\sqrt{a x^2+b x^3+c x^4}} \, dx","Int[x^3/Sqrt[a*x^2 + b*x^3 + c*x^4],x]","\frac{x \left(3 b^2-4 a c\right) \sqrt{a+b x+c x^2} \tanh ^{-1}\left(\frac{b+2 c x}{2 \sqrt{c} \sqrt{a+b x+c x^2}}\right)}{8 c^{5/2} \sqrt{a x^2+b x^3+c x^4}}-\frac{3 b \sqrt{a x^2+b x^3+c x^4}}{4 c^2 x}+\frac{\sqrt{a x^2+b x^3+c x^4}}{2 c}","\frac{x \left(3 b^2-4 a c\right) \sqrt{a+b x+c x^2} \tanh ^{-1}\left(\frac{b+2 c x}{2 \sqrt{c} \sqrt{a+b x+c x^2}}\right)}{8 c^{5/2} \sqrt{a x^2+b x^3+c x^4}}-\frac{3 b \sqrt{a x^2+b x^3+c x^4}}{4 c^2 x}+\frac{\sqrt{a x^2+b x^3+c x^4}}{2 c}",1,"Sqrt[a*x^2 + b*x^3 + c*x^4]/(2*c) - (3*b*Sqrt[a*x^2 + b*x^3 + c*x^4])/(4*c^2*x) + ((3*b^2 - 4*a*c)*x*Sqrt[a + b*x + c*x^2]*ArcTanh[(b + 2*c*x)/(2*Sqrt[c]*Sqrt[a + b*x + c*x^2])])/(8*c^(5/2)*Sqrt[a*x^2 + b*x^3 + c*x^4])","A",6,6,24,0.2500,1,"{1928, 1949, 12, 1914, 621, 206}"
50,1,103,0,0.0776804,"\int \frac{x^2}{\sqrt{a x^2+b x^3+c x^4}} \, dx","Int[x^2/Sqrt[a*x^2 + b*x^3 + c*x^4],x]","\frac{\sqrt{a x^2+b x^3+c x^4}}{c x}-\frac{b x \sqrt{a+b x+c x^2} \tanh ^{-1}\left(\frac{b+2 c x}{2 \sqrt{c} \sqrt{a+b x+c x^2}}\right)}{2 c^{3/2} \sqrt{a x^2+b x^3+c x^4}}","\frac{\sqrt{a x^2+b x^3+c x^4}}{c x}-\frac{b x \sqrt{a+b x+c x^2} \tanh ^{-1}\left(\frac{b+2 c x}{2 \sqrt{c} \sqrt{a+b x+c x^2}}\right)}{2 c^{3/2} \sqrt{a x^2+b x^3+c x^4}}",1,"Sqrt[a*x^2 + b*x^3 + c*x^4]/(c*x) - (b*x*Sqrt[a + b*x + c*x^2]*ArcTanh[(b + 2*c*x)/(2*Sqrt[c]*Sqrt[a + b*x + c*x^2])])/(2*c^(3/2)*Sqrt[a*x^2 + b*x^3 + c*x^4])","A",4,4,24,0.1667,1,"{1917, 1914, 621, 206}"
51,1,71,0,0.0366343,"\int \frac{x}{\sqrt{a x^2+b x^3+c x^4}} \, dx","Int[x/Sqrt[a*x^2 + b*x^3 + c*x^4],x]","\frac{x \sqrt{a+b x+c x^2} \tanh ^{-1}\left(\frac{b+2 c x}{2 \sqrt{c} \sqrt{a+b x+c x^2}}\right)}{\sqrt{c} \sqrt{a x^2+b x^3+c x^4}}","\frac{x \sqrt{a+b x+c x^2} \tanh ^{-1}\left(\frac{b+2 c x}{2 \sqrt{c} \sqrt{a+b x+c x^2}}\right)}{\sqrt{c} \sqrt{a x^2+b x^3+c x^4}}",1,"(x*Sqrt[a + b*x + c*x^2]*ArcTanh[(b + 2*c*x)/(2*Sqrt[c]*Sqrt[a + b*x + c*x^2])])/(Sqrt[c]*Sqrt[a*x^2 + b*x^3 + c*x^4])","A",3,3,22,0.1364,1,"{1914, 621, 206}"
52,1,45,0,0.0158112,"\int \frac{1}{\sqrt{a x^2+b x^3+c x^4}} \, dx","Int[1/Sqrt[a*x^2 + b*x^3 + c*x^4],x]","-\frac{\tanh ^{-1}\left(\frac{x (2 a+b x)}{2 \sqrt{a} \sqrt{a x^2+b x^3+c x^4}}\right)}{\sqrt{a}}","-\frac{\tanh ^{-1}\left(\frac{x (2 a+b x)}{2 \sqrt{a} \sqrt{a x^2+b x^3+c x^4}}\right)}{\sqrt{a}}",1,"-(ArcTanh[(x*(2*a + b*x))/(2*Sqrt[a]*Sqrt[a*x^2 + b*x^3 + c*x^4])]/Sqrt[a])","A",2,2,20,0.1000,1,"{1904, 206}"
53,1,77,0,0.0540936,"\int \frac{1}{x \sqrt{a x^2+b x^3+c x^4}} \, dx","Int[1/(x*Sqrt[a*x^2 + b*x^3 + c*x^4]),x]","\frac{b \tanh ^{-1}\left(\frac{x (2 a+b x)}{2 \sqrt{a} \sqrt{a x^2+b x^3+c x^4}}\right)}{2 a^{3/2}}-\frac{\sqrt{a x^2+b x^3+c x^4}}{a x^2}","\frac{b \tanh ^{-1}\left(\frac{x (2 a+b x)}{2 \sqrt{a} \sqrt{a x^2+b x^3+c x^4}}\right)}{2 a^{3/2}}-\frac{\sqrt{a x^2+b x^3+c x^4}}{a x^2}",1,"-(Sqrt[a*x^2 + b*x^3 + c*x^4]/(a*x^2)) + (b*ArcTanh[(x*(2*a + b*x))/(2*Sqrt[a]*Sqrt[a*x^2 + b*x^3 + c*x^4])])/(2*a^(3/2))","A",3,3,24,0.1250,1,"{1927, 1904, 206}"
54,1,119,0,0.1486562,"\int \frac{1}{x^2 \sqrt{a x^2+b x^3+c x^4}} \, dx","Int[1/(x^2*Sqrt[a*x^2 + b*x^3 + c*x^4]),x]","-\frac{\left(3 b^2-4 a c\right) \tanh ^{-1}\left(\frac{x (2 a+b x)}{2 \sqrt{a} \sqrt{a x^2+b x^3+c x^4}}\right)}{8 a^{5/2}}+\frac{3 b \sqrt{a x^2+b x^3+c x^4}}{4 a^2 x^2}-\frac{\sqrt{a x^2+b x^3+c x^4}}{2 a x^3}","-\frac{\left(3 b^2-4 a c\right) \tanh ^{-1}\left(\frac{x (2 a+b x)}{2 \sqrt{a} \sqrt{a x^2+b x^3+c x^4}}\right)}{8 a^{5/2}}+\frac{3 b \sqrt{a x^2+b x^3+c x^4}}{4 a^2 x^2}-\frac{\sqrt{a x^2+b x^3+c x^4}}{2 a x^3}",1,"-Sqrt[a*x^2 + b*x^3 + c*x^4]/(2*a*x^3) + (3*b*Sqrt[a*x^2 + b*x^3 + c*x^4])/(4*a^2*x^2) - ((3*b^2 - 4*a*c)*ArcTanh[(x*(2*a + b*x))/(2*Sqrt[a]*Sqrt[a*x^2 + b*x^3 + c*x^4])])/(8*a^(5/2))","A",5,5,24,0.2083,1,"{1929, 1951, 12, 1904, 206}"
55,1,262,0,0.50583,"\int \frac{x^7}{\left(a x^2+b x^3+c x^4\right)^{3/2}} \, dx","Int[x^7/(a*x^2 + b*x^3 + c*x^4)^(3/2),x]","\frac{\left(5 b^2-12 a c\right) \sqrt{a x^2+b x^3+c x^4}}{2 c^2 \left(b^2-4 a c\right)}-\frac{b \left(15 b^2-52 a c\right) \sqrt{a x^2+b x^3+c x^4}}{4 c^3 x \left(b^2-4 a c\right)}+\frac{3 x \left(5 b^2-4 a c\right) \sqrt{a+b x+c x^2} \tanh ^{-1}\left(\frac{b+2 c x}{2 \sqrt{c} \sqrt{a+b x+c x^2}}\right)}{8 c^{7/2} \sqrt{a x^2+b x^3+c x^4}}+\frac{2 x^4 (2 a+b x)}{\left(b^2-4 a c\right) \sqrt{a x^2+b x^3+c x^4}}-\frac{2 b x \sqrt{a x^2+b x^3+c x^4}}{c \left(b^2-4 a c\right)}","\frac{\left(5 b^2-12 a c\right) \sqrt{a x^2+b x^3+c x^4}}{2 c^2 \left(b^2-4 a c\right)}-\frac{b \left(15 b^2-52 a c\right) \sqrt{a x^2+b x^3+c x^4}}{4 c^3 x \left(b^2-4 a c\right)}+\frac{3 x \left(5 b^2-4 a c\right) \sqrt{a+b x+c x^2} \tanh ^{-1}\left(\frac{b+2 c x}{2 \sqrt{c} \sqrt{a+b x+c x^2}}\right)}{8 c^{7/2} \sqrt{a x^2+b x^3+c x^4}}+\frac{2 x^4 (2 a+b x)}{\left(b^2-4 a c\right) \sqrt{a x^2+b x^3+c x^4}}-\frac{2 b x \sqrt{a x^2+b x^3+c x^4}}{c \left(b^2-4 a c\right)}",1,"(2*x^4*(2*a + b*x))/((b^2 - 4*a*c)*Sqrt[a*x^2 + b*x^3 + c*x^4]) + ((5*b^2 - 12*a*c)*Sqrt[a*x^2 + b*x^3 + c*x^4])/(2*c^2*(b^2 - 4*a*c)) - (b*(15*b^2 - 52*a*c)*Sqrt[a*x^2 + b*x^3 + c*x^4])/(4*c^3*(b^2 - 4*a*c)*x) - (2*b*x*Sqrt[a*x^2 + b*x^3 + c*x^4])/(c*(b^2 - 4*a*c)) + (3*(5*b^2 - 4*a*c)*x*Sqrt[a + b*x + c*x^2]*ArcTanh[(b + 2*c*x)/(2*Sqrt[c]*Sqrt[a + b*x + c*x^2])])/(8*c^(7/2)*Sqrt[a*x^2 + b*x^3 + c*x^4])","A",8,6,24,0.2500,1,"{1923, 1949, 12, 1914, 621, 206}"
56,1,201,0,0.3046594,"\int \frac{x^6}{\left(a x^2+b x^3+c x^4\right)^{3/2}} \, dx","Int[x^6/(a*x^2 + b*x^3 + c*x^4)^(3/2),x]","\frac{\left(3 b^2-8 a c\right) \sqrt{a x^2+b x^3+c x^4}}{c^2 x \left(b^2-4 a c\right)}+\frac{2 x^3 (2 a+b x)}{\left(b^2-4 a c\right) \sqrt{a x^2+b x^3+c x^4}}-\frac{2 b \sqrt{a x^2+b x^3+c x^4}}{c \left(b^2-4 a c\right)}-\frac{3 b x \sqrt{a+b x+c x^2} \tanh ^{-1}\left(\frac{b+2 c x}{2 \sqrt{c} \sqrt{a+b x+c x^2}}\right)}{2 c^{5/2} \sqrt{a x^2+b x^3+c x^4}}","\frac{\left(3 b^2-8 a c\right) \sqrt{a x^2+b x^3+c x^4}}{c^2 x \left(b^2-4 a c\right)}+\frac{2 x^3 (2 a+b x)}{\left(b^2-4 a c\right) \sqrt{a x^2+b x^3+c x^4}}-\frac{2 b \sqrt{a x^2+b x^3+c x^4}}{c \left(b^2-4 a c\right)}-\frac{3 b x \sqrt{a+b x+c x^2} \tanh ^{-1}\left(\frac{b+2 c x}{2 \sqrt{c} \sqrt{a+b x+c x^2}}\right)}{2 c^{5/2} \sqrt{a x^2+b x^3+c x^4}}",1,"(2*x^3*(2*a + b*x))/((b^2 - 4*a*c)*Sqrt[a*x^2 + b*x^3 + c*x^4]) - (2*b*Sqrt[a*x^2 + b*x^3 + c*x^4])/(c*(b^2 - 4*a*c)) + ((3*b^2 - 8*a*c)*Sqrt[a*x^2 + b*x^3 + c*x^4])/(c^2*(b^2 - 4*a*c)*x) - (3*b*x*Sqrt[a + b*x + c*x^2]*ArcTanh[(b + 2*c*x)/(2*Sqrt[c]*Sqrt[a + b*x + c*x^2])])/(2*c^(5/2)*Sqrt[a*x^2 + b*x^3 + c*x^4])","A",7,6,24,0.2500,1,"{1923, 1949, 12, 1914, 621, 206}"
57,1,153,0,0.1752928,"\int \frac{x^5}{\left(a x^2+b x^3+c x^4\right)^{3/2}} \, dx","Int[x^5/(a*x^2 + b*x^3 + c*x^4)^(3/2),x]","\frac{2 x^2 (2 a+b x)}{\left(b^2-4 a c\right) \sqrt{a x^2+b x^3+c x^4}}-\frac{2 b \sqrt{a x^2+b x^3+c x^4}}{c x \left(b^2-4 a c\right)}+\frac{x \sqrt{a+b x+c x^2} \tanh ^{-1}\left(\frac{b+2 c x}{2 \sqrt{c} \sqrt{a+b x+c x^2}}\right)}{c^{3/2} \sqrt{a x^2+b x^3+c x^4}}","\frac{2 x^2 (2 a+b x)}{\left(b^2-4 a c\right) \sqrt{a x^2+b x^3+c x^4}}-\frac{2 b \sqrt{a x^2+b x^3+c x^4}}{c x \left(b^2-4 a c\right)}+\frac{x \sqrt{a+b x+c x^2} \tanh ^{-1}\left(\frac{b+2 c x}{2 \sqrt{c} \sqrt{a+b x+c x^2}}\right)}{c^{3/2} \sqrt{a x^2+b x^3+c x^4}}",1,"(2*x^2*(2*a + b*x))/((b^2 - 4*a*c)*Sqrt[a*x^2 + b*x^3 + c*x^4]) - (2*b*Sqrt[a*x^2 + b*x^3 + c*x^4])/(c*(b^2 - 4*a*c)*x) + (x*Sqrt[a + b*x + c*x^2]*ArcTanh[(b + 2*c*x)/(2*Sqrt[c]*Sqrt[a + b*x + c*x^2])])/(c^(3/2)*Sqrt[a*x^2 + b*x^3 + c*x^4])","A",6,6,24,0.2500,1,"{1923, 1949, 12, 1914, 621, 206}"
58,1,40,0,0.0399566,"\int \frac{x^4}{\left(a x^2+b x^3+c x^4\right)^{3/2}} \, dx","Int[x^4/(a*x^2 + b*x^3 + c*x^4)^(3/2),x]","\frac{2 x (2 a+b x)}{\left(b^2-4 a c\right) \sqrt{a x^2+b x^3+c x^4}}","\frac{2 x (2 a+b x)}{\left(b^2-4 a c\right) \sqrt{a x^2+b x^3+c x^4}}",1,"(2*x*(2*a + b*x))/((b^2 - 4*a*c)*Sqrt[a*x^2 + b*x^3 + c*x^4])","A",1,1,24,0.04167,1,"{1916}"
59,1,39,0,0.0402122,"\int \frac{x^3}{\left(a x^2+b x^3+c x^4\right)^{3/2}} \, dx","Int[x^3/(a*x^2 + b*x^3 + c*x^4)^(3/2),x]","-\frac{2 x (b+2 c x)}{\left(b^2-4 a c\right) \sqrt{a x^2+b x^3+c x^4}}","-\frac{2 x (b+2 c x)}{\left(b^2-4 a c\right) \sqrt{a x^2+b x^3+c x^4}}",1,"(-2*x*(b + 2*c*x))/((b^2 - 4*a*c)*Sqrt[a*x^2 + b*x^3 + c*x^4])","A",1,1,24,0.04167,1,"{1915}"
60,1,94,0,0.0676333,"\int \frac{x^2}{\left(a x^2+b x^3+c x^4\right)^{3/2}} \, dx","Int[x^2/(a*x^2 + b*x^3 + c*x^4)^(3/2),x]","\frac{2 x \left(-2 a c+b^2+b c x\right)}{a \left(b^2-4 a c\right) \sqrt{a x^2+b x^3+c x^4}}-\frac{\tanh ^{-1}\left(\frac{x (2 a+b x)}{2 \sqrt{a} \sqrt{a x^2+b x^3+c x^4}}\right)}{a^{3/2}}","\frac{2 x \left(-2 a c+b^2+b c x\right)}{a \left(b^2-4 a c\right) \sqrt{a x^2+b x^3+c x^4}}-\frac{\tanh ^{-1}\left(\frac{x (2 a+b x)}{2 \sqrt{a} \sqrt{a x^2+b x^3+c x^4}}\right)}{a^{3/2}}",1,"(2*x*(b^2 - 2*a*c + b*c*x))/(a*(b^2 - 4*a*c)*Sqrt[a*x^2 + b*x^3 + c*x^4]) - ArcTanh[(x*(2*a + b*x))/(2*Sqrt[a]*Sqrt[a*x^2 + b*x^3 + c*x^4])]/a^(3/2)","A",3,3,24,0.1250,1,"{1922, 1904, 206}"
61,1,144,0,0.1631714,"\int \frac{x}{\left(a x^2+b x^3+c x^4\right)^{3/2}} \, dx","Int[x/(a*x^2 + b*x^3 + c*x^4)^(3/2),x]","-\frac{\left(3 b^2-8 a c\right) \sqrt{a x^2+b x^3+c x^4}}{a^2 x^2 \left(b^2-4 a c\right)}+\frac{3 b \tanh ^{-1}\left(\frac{x (2 a+b x)}{2 \sqrt{a} \sqrt{a x^2+b x^3+c x^4}}\right)}{2 a^{5/2}}+\frac{2 \left(-2 a c+b^2+b c x\right)}{a \left(b^2-4 a c\right) \sqrt{a x^2+b x^3+c x^4}}","-\frac{\left(3 b^2-8 a c\right) \sqrt{a x^2+b x^3+c x^4}}{a^2 x^2 \left(b^2-4 a c\right)}+\frac{3 b \tanh ^{-1}\left(\frac{x (2 a+b x)}{2 \sqrt{a} \sqrt{a x^2+b x^3+c x^4}}\right)}{2 a^{5/2}}+\frac{2 \left(-2 a c+b^2+b c x\right)}{a \left(b^2-4 a c\right) \sqrt{a x^2+b x^3+c x^4}}",1,"(2*(b^2 - 2*a*c + b*c*x))/(a*(b^2 - 4*a*c)*Sqrt[a*x^2 + b*x^3 + c*x^4]) - ((3*b^2 - 8*a*c)*Sqrt[a*x^2 + b*x^3 + c*x^4])/(a^2*(b^2 - 4*a*c)*x^2) + (3*b*ArcTanh[(x*(2*a + b*x))/(2*Sqrt[a]*Sqrt[a*x^2 + b*x^3 + c*x^4])])/(2*a^(5/2))","A",5,5,22,0.2273,1,"{1924, 1951, 12, 1904, 206}"
62,1,209,0,0.2869886,"\int \frac{1}{\left(a x^2+b x^3+c x^4\right)^{3/2}} \, dx","Int[(a*x^2 + b*x^3 + c*x^4)^(-3/2),x]","\frac{b \left(15 b^2-52 a c\right) \sqrt{a x^2+b x^3+c x^4}}{4 a^3 x^2 \left(b^2-4 a c\right)}-\frac{\left(5 b^2-12 a c\right) \sqrt{a x^2+b x^3+c x^4}}{2 a^2 x^3 \left(b^2-4 a c\right)}-\frac{3 \left(5 b^2-4 a c\right) \tanh ^{-1}\left(\frac{x (2 a+b x)}{2 \sqrt{a} \sqrt{a x^2+b x^3+c x^4}}\right)}{8 a^{7/2}}+\frac{2 \left(-2 a c+b^2+b c x\right)}{a x \left(b^2-4 a c\right) \sqrt{a x^2+b x^3+c x^4}}","\frac{b \left(15 b^2-52 a c\right) \sqrt{a x^2+b x^3+c x^4}}{4 a^3 x^2 \left(b^2-4 a c\right)}-\frac{\left(5 b^2-12 a c\right) \sqrt{a x^2+b x^3+c x^4}}{2 a^2 x^3 \left(b^2-4 a c\right)}-\frac{3 \left(5 b^2-4 a c\right) \tanh ^{-1}\left(\frac{x (2 a+b x)}{2 \sqrt{a} \sqrt{a x^2+b x^3+c x^4}}\right)}{8 a^{7/2}}+\frac{2 \left(-2 a c+b^2+b c x\right)}{a x \left(b^2-4 a c\right) \sqrt{a x^2+b x^3+c x^4}}",1,"(2*(b^2 - 2*a*c + b*c*x))/(a*(b^2 - 4*a*c)*x*Sqrt[a*x^2 + b*x^3 + c*x^4]) - ((5*b^2 - 12*a*c)*Sqrt[a*x^2 + b*x^3 + c*x^4])/(2*a^2*(b^2 - 4*a*c)*x^3) + (b*(15*b^2 - 52*a*c)*Sqrt[a*x^2 + b*x^3 + c*x^4])/(4*a^3*(b^2 - 4*a*c)*x^2) - (3*(5*b^2 - 4*a*c)*ArcTanh[(x*(2*a + b*x))/(2*Sqrt[a]*Sqrt[a*x^2 + b*x^3 + c*x^4])])/(8*a^(7/2))","A",6,5,20,0.2500,1,"{1907, 1951, 12, 1904, 206}"
63,1,271,0,0.4524494,"\int \frac{1}{x \left(a x^2+b x^3+c x^4\right)^{3/2}} \, dx","Int[1/(x*(a*x^2 + b*x^3 + c*x^4)^(3/2)),x]","-\frac{\left(256 a^2 c^2-460 a b^2 c+105 b^4\right) \sqrt{a x^2+b x^3+c x^4}}{24 a^4 x^2 \left(b^2-4 a c\right)}+\frac{b \left(35 b^2-116 a c\right) \sqrt{a x^2+b x^3+c x^4}}{12 a^3 x^3 \left(b^2-4 a c\right)}-\frac{\left(7 b^2-16 a c\right) \sqrt{a x^2+b x^3+c x^4}}{3 a^2 x^4 \left(b^2-4 a c\right)}+\frac{5 b \left(7 b^2-12 a c\right) \tanh ^{-1}\left(\frac{x (2 a+b x)}{2 \sqrt{a} \sqrt{a x^2+b x^3+c x^4}}\right)}{16 a^{9/2}}+\frac{2 \left(-2 a c+b^2+b c x\right)}{a x^2 \left(b^2-4 a c\right) \sqrt{a x^2+b x^3+c x^4}}","-\frac{\left(256 a^2 c^2-460 a b^2 c+105 b^4\right) \sqrt{a x^2+b x^3+c x^4}}{24 a^4 x^2 \left(b^2-4 a c\right)}+\frac{b \left(35 b^2-116 a c\right) \sqrt{a x^2+b x^3+c x^4}}{12 a^3 x^3 \left(b^2-4 a c\right)}-\frac{\left(7 b^2-16 a c\right) \sqrt{a x^2+b x^3+c x^4}}{3 a^2 x^4 \left(b^2-4 a c\right)}+\frac{5 b \left(7 b^2-12 a c\right) \tanh ^{-1}\left(\frac{x (2 a+b x)}{2 \sqrt{a} \sqrt{a x^2+b x^3+c x^4}}\right)}{16 a^{9/2}}+\frac{2 \left(-2 a c+b^2+b c x\right)}{a x^2 \left(b^2-4 a c\right) \sqrt{a x^2+b x^3+c x^4}}",1,"(2*(b^2 - 2*a*c + b*c*x))/(a*(b^2 - 4*a*c)*x^2*Sqrt[a*x^2 + b*x^3 + c*x^4]) - ((7*b^2 - 16*a*c)*Sqrt[a*x^2 + b*x^3 + c*x^4])/(3*a^2*(b^2 - 4*a*c)*x^4) + (b*(35*b^2 - 116*a*c)*Sqrt[a*x^2 + b*x^3 + c*x^4])/(12*a^3*(b^2 - 4*a*c)*x^3) - ((105*b^4 - 460*a*b^2*c + 256*a^2*c^2)*Sqrt[a*x^2 + b*x^3 + c*x^4])/(24*a^4*(b^2 - 4*a*c)*x^2) + (5*b*(7*b^2 - 12*a*c)*ArcTanh[(x*(2*a + b*x))/(2*Sqrt[a]*Sqrt[a*x^2 + b*x^3 + c*x^4])])/(16*a^(9/2))","A",7,5,24,0.2083,1,"{1924, 1951, 12, 1904, 206}"
64,1,343,0,0.6205513,"\int \frac{1}{x^2 \left(a x^2+b x^3+c x^4\right)^{3/2}} \, dx","Int[1/(x^2*(a*x^2 + b*x^3 + c*x^4)^(3/2)),x]","\frac{b \left(1808 a^2 c^2-1680 a b^2 c+315 b^4\right) \sqrt{a x^2+b x^3+c x^4}}{64 a^5 x^2 \left(b^2-4 a c\right)}-\frac{\left(240 a^2 c^2-448 a b^2 c+105 b^4\right) \sqrt{a x^2+b x^3+c x^4}}{32 a^4 x^3 \left(b^2-4 a c\right)}-\frac{15 \left(16 a^2 c^2-56 a b^2 c+21 b^4\right) \tanh ^{-1}\left(\frac{x (2 a+b x)}{2 \sqrt{a} \sqrt{a x^2+b x^3+c x^4}}\right)}{128 a^{11/2}}+\frac{b \left(21 b^2-68 a c\right) \sqrt{a x^2+b x^3+c x^4}}{8 a^3 x^4 \left(b^2-4 a c\right)}-\frac{\left(9 b^2-20 a c\right) \sqrt{a x^2+b x^3+c x^4}}{4 a^2 x^5 \left(b^2-4 a c\right)}+\frac{2 \left(-2 a c+b^2+b c x\right)}{a x^3 \left(b^2-4 a c\right) \sqrt{a x^2+b x^3+c x^4}}","\frac{b \left(1808 a^2 c^2-1680 a b^2 c+315 b^4\right) \sqrt{a x^2+b x^3+c x^4}}{64 a^5 x^2 \left(b^2-4 a c\right)}-\frac{\left(240 a^2 c^2-448 a b^2 c+105 b^4\right) \sqrt{a x^2+b x^3+c x^4}}{32 a^4 x^3 \left(b^2-4 a c\right)}-\frac{15 \left(16 a^2 c^2-56 a b^2 c+21 b^4\right) \tanh ^{-1}\left(\frac{x (2 a+b x)}{2 \sqrt{a} \sqrt{a x^2+b x^3+c x^4}}\right)}{128 a^{11/2}}+\frac{b \left(21 b^2-68 a c\right) \sqrt{a x^2+b x^3+c x^4}}{8 a^3 x^4 \left(b^2-4 a c\right)}-\frac{\left(9 b^2-20 a c\right) \sqrt{a x^2+b x^3+c x^4}}{4 a^2 x^5 \left(b^2-4 a c\right)}+\frac{2 \left(-2 a c+b^2+b c x\right)}{a x^3 \left(b^2-4 a c\right) \sqrt{a x^2+b x^3+c x^4}}",1,"(2*(b^2 - 2*a*c + b*c*x))/(a*(b^2 - 4*a*c)*x^3*Sqrt[a*x^2 + b*x^3 + c*x^4]) - ((9*b^2 - 20*a*c)*Sqrt[a*x^2 + b*x^3 + c*x^4])/(4*a^2*(b^2 - 4*a*c)*x^5) + (b*(21*b^2 - 68*a*c)*Sqrt[a*x^2 + b*x^3 + c*x^4])/(8*a^3*(b^2 - 4*a*c)*x^4) - ((105*b^4 - 448*a*b^2*c + 240*a^2*c^2)*Sqrt[a*x^2 + b*x^3 + c*x^4])/(32*a^4*(b^2 - 4*a*c)*x^3) + (b*(315*b^4 - 1680*a*b^2*c + 1808*a^2*c^2)*Sqrt[a*x^2 + b*x^3 + c*x^4])/(64*a^5*(b^2 - 4*a*c)*x^2) - (15*(21*b^4 - 56*a*b^2*c + 16*a^2*c^2)*ArcTanh[(x*(2*a + b*x))/(2*Sqrt[a]*Sqrt[a*x^2 + b*x^3 + c*x^4])])/(128*a^(11/2))","A",8,5,24,0.2083,1,"{1924, 1951, 12, 1904, 206}"
65,1,37,0,0.0129212,"\int x^m \left(a x+b x^3+c x^5\right) \, dx","Int[x^m*(a*x + b*x^3 + c*x^5),x]","\frac{a x^{m+2}}{m+2}+\frac{b x^{m+4}}{m+4}+\frac{c x^{m+6}}{m+6}","\frac{a x^{m+2}}{m+2}+\frac{b x^{m+4}}{m+4}+\frac{c x^{m+6}}{m+6}",1,"(a*x^(2 + m))/(2 + m) + (b*x^(4 + m))/(4 + m) + (c*x^(6 + m))/(6 + m)","A",2,1,18,0.05556,1,"{14}"
66,1,25,0,0.0078675,"\int x^2 \left(a x+b x^3+c x^5\right) \, dx","Int[x^2*(a*x + b*x^3 + c*x^5),x]","\frac{a x^4}{4}+\frac{b x^6}{6}+\frac{c x^8}{8}","\frac{a x^4}{4}+\frac{b x^6}{6}+\frac{c x^8}{8}",1,"(a*x^4)/4 + (b*x^6)/6 + (c*x^8)/8","A",2,1,18,0.05556,1,"{14}"
67,1,25,0,0.0072531,"\int x \left(a x+b x^3+c x^5\right) \, dx","Int[x*(a*x + b*x^3 + c*x^5),x]","\frac{a x^3}{3}+\frac{b x^5}{5}+\frac{c x^7}{7}","\frac{a x^3}{3}+\frac{b x^5}{5}+\frac{c x^7}{7}",1,"(a*x^3)/3 + (b*x^5)/5 + (c*x^7)/7","A",2,1,16,0.06250,1,"{14}"
68,1,25,0,0.0044085,"\int \left(a x+b x^3+c x^5\right) \, dx","Int[a*x + b*x^3 + c*x^5,x]","\frac{a x^2}{2}+\frac{b x^4}{4}+\frac{c x^6}{6}","\frac{a x^2}{2}+\frac{b x^4}{4}+\frac{c x^6}{6}",1,"(a*x^2)/2 + (b*x^4)/4 + (c*x^6)/6","A",1,0,14,0,1,"{}"
69,1,20,0,0.0056522,"\int \frac{a x+b x^3+c x^5}{x} \, dx","Int[(a*x + b*x^3 + c*x^5)/x,x]","a x+\frac{b x^3}{3}+\frac{c x^5}{5}","a x+\frac{b x^3}{3}+\frac{c x^5}{5}",1,"a*x + (b*x^3)/3 + (c*x^5)/5","A",2,1,18,0.05556,1,"{14}"
70,1,21,0,0.0081022,"\int \frac{a x+b x^3+c x^5}{x^2} \, dx","Int[(a*x + b*x^3 + c*x^5)/x^2,x]","a \log (x)+\frac{b x^2}{2}+\frac{c x^4}{4}","a \log (x)+\frac{b x^2}{2}+\frac{c x^4}{4}",1,"(b*x^2)/2 + (c*x^4)/4 + a*Log[x]","A",2,1,18,0.05556,1,"{14}"
71,1,18,0,0.0068819,"\int \frac{a x+b x^3+c x^5}{x^3} \, dx","Int[(a*x + b*x^3 + c*x^5)/x^3,x]","-\frac{a}{x}+b x+\frac{c x^3}{3}","-\frac{a}{x}+b x+\frac{c x^3}{3}",1,"-(a/x) + b*x + (c*x^3)/3","A",2,1,18,0.05556,1,"{14}"
72,1,76,0,0.0458617,"\int x^m \left(a x+b x^3+c x^5\right)^2 \, dx","Int[x^m*(a*x + b*x^3 + c*x^5)^2,x]","\frac{a^2 x^{m+3}}{m+3}+\frac{x^{m+7} \left(2 a c+b^2\right)}{m+7}+\frac{2 a b x^{m+5}}{m+5}+\frac{2 b c x^{m+9}}{m+9}+\frac{c^2 x^{m+11}}{m+11}","\frac{a^2 x^{m+3}}{m+3}+\frac{x^{m+7} \left(2 a c+b^2\right)}{m+7}+\frac{2 a b x^{m+5}}{m+5}+\frac{2 b c x^{m+9}}{m+9}+\frac{c^2 x^{m+11}}{m+11}",1,"(a^2*x^(3 + m))/(3 + m) + (2*a*b*x^(5 + m))/(5 + m) + ((b^2 + 2*a*c)*x^(7 + m))/(7 + m) + (2*b*c*x^(9 + m))/(9 + m) + (c^2*x^(11 + m))/(11 + m)","A",3,2,20,0.1000,1,"{1585, 1108}"
73,1,54,0,0.0360609,"\int x^2 \left(a x+b x^3+c x^5\right)^2 \, dx","Int[x^2*(a*x + b*x^3 + c*x^5)^2,x]","\frac{a^2 x^5}{5}+\frac{1}{9} x^9 \left(2 a c+b^2\right)+\frac{2}{7} a b x^7+\frac{2}{11} b c x^{11}+\frac{c^2 x^{13}}{13}","\frac{a^2 x^5}{5}+\frac{1}{9} x^9 \left(2 a c+b^2\right)+\frac{2}{7} a b x^7+\frac{2}{11} b c x^{11}+\frac{c^2 x^{13}}{13}",1,"(a^2*x^5)/5 + (2*a*b*x^7)/7 + ((b^2 + 2*a*c)*x^9)/9 + (2*b*c*x^11)/11 + (c^2*x^13)/13","A",3,2,20,0.1000,1,"{1585, 1108}"
74,1,54,0,0.0544296,"\int x \left(a x+b x^3+c x^5\right)^2 \, dx","Int[x*(a*x + b*x^3 + c*x^5)^2,x]","\frac{a^2 x^4}{4}+\frac{1}{8} x^8 \left(2 a c+b^2\right)+\frac{1}{3} a b x^6+\frac{1}{5} b c x^{10}+\frac{c^2 x^{12}}{12}","\frac{a^2 x^4}{4}+\frac{1}{8} x^8 \left(2 a c+b^2\right)+\frac{1}{3} a b x^6+\frac{1}{5} b c x^{10}+\frac{c^2 x^{12}}{12}",1,"(a^2*x^4)/4 + (a*b*x^6)/3 + ((b^2 + 2*a*c)*x^8)/8 + (b*c*x^10)/5 + (c^2*x^12)/12","A",4,3,18,0.1667,1,"{1585, 1114, 631}"
75,1,54,0,0.0263768,"\int \left(a x+b x^3+c x^5\right)^2 \, dx","Int[(a*x + b*x^3 + c*x^5)^2,x]","\frac{a^2 x^3}{3}+\frac{1}{7} x^7 \left(2 a c+b^2\right)+\frac{2}{5} a b x^5+\frac{2}{9} b c x^9+\frac{c^2 x^{11}}{11}","\frac{a^2 x^3}{3}+\frac{1}{7} x^7 \left(2 a c+b^2\right)+\frac{2}{5} a b x^5+\frac{2}{9} b c x^9+\frac{c^2 x^{11}}{11}",1,"(a^2*x^3)/3 + (2*a*b*x^5)/5 + ((b^2 + 2*a*c)*x^7)/7 + (2*b*c*x^9)/9 + (c^2*x^11)/11","A",3,2,16,0.1250,1,"{1594, 1108}"
76,1,54,0,0.0456916,"\int \frac{\left(a x+b x^3+c x^5\right)^2}{x} \, dx","Int[(a*x + b*x^3 + c*x^5)^2/x,x]","\frac{a^2 x^2}{2}+\frac{1}{6} x^6 \left(2 a c+b^2\right)+\frac{1}{2} a b x^4+\frac{1}{4} b c x^8+\frac{c^2 x^{10}}{10}","\frac{a^2 x^2}{2}+\frac{1}{6} x^6 \left(2 a c+b^2\right)+\frac{1}{2} a b x^4+\frac{1}{4} b c x^8+\frac{c^2 x^{10}}{10}",1,"(a^2*x^2)/2 + (a*b*x^4)/2 + ((b^2 + 2*a*c)*x^6)/6 + (b*c*x^8)/4 + (c^2*x^10)/10","A",4,3,20,0.1500,1,"{1585, 1107, 611}"
77,1,49,0,0.0272706,"\int \frac{\left(a x+b x^3+c x^5\right)^2}{x^2} \, dx","Int[(a*x + b*x^3 + c*x^5)^2/x^2,x]","a^2 x+\frac{1}{5} x^5 \left(2 a c+b^2\right)+\frac{2}{3} a b x^3+\frac{2}{7} b c x^7+\frac{c^2 x^9}{9}","a^2 x+\frac{1}{5} x^5 \left(2 a c+b^2\right)+\frac{2}{3} a b x^3+\frac{2}{7} b c x^7+\frac{c^2 x^9}{9}",1,"a^2*x + (2*a*b*x^3)/3 + ((b^2 + 2*a*c)*x^5)/5 + (2*b*c*x^7)/7 + (c^2*x^9)/9","A",3,2,20,0.1000,1,"{1585, 1090}"
78,1,100,0,0.1217376,"\int \frac{x^8}{a x+b x^3+c x^5} \, dx","Int[x^8/(a*x + b*x^3 + c*x^5),x]","\frac{\left(b^2-a c\right) \log \left(a+b x^2+c x^4\right)}{4 c^3}+\frac{b \left(b^2-3 a c\right) \tanh ^{-1}\left(\frac{b+2 c x^2}{\sqrt{b^2-4 a c}}\right)}{2 c^3 \sqrt{b^2-4 a c}}-\frac{b x^2}{2 c^2}+\frac{x^4}{4 c}","\frac{\left(b^2-a c\right) \log \left(a+b x^2+c x^4\right)}{4 c^3}+\frac{b \left(b^2-3 a c\right) \tanh ^{-1}\left(\frac{b+2 c x^2}{\sqrt{b^2-4 a c}}\right)}{2 c^3 \sqrt{b^2-4 a c}}-\frac{b x^2}{2 c^2}+\frac{x^4}{4 c}",1,"-(b*x^2)/(2*c^2) + x^4/(4*c) + (b*(b^2 - 3*a*c)*ArcTanh[(b + 2*c*x^2)/Sqrt[b^2 - 4*a*c]])/(2*c^3*Sqrt[b^2 - 4*a*c]) + ((b^2 - a*c)*Log[a + b*x^2 + c*x^4])/(4*c^3)","A",8,7,20,0.3500,1,"{1585, 1114, 701, 634, 618, 206, 628}"
79,1,203,0,0.6024927,"\int \frac{x^7}{a x+b x^3+c x^5} \, dx","Int[x^7/(a*x + b*x^3 + c*x^5),x]","\frac{\left(-\frac{b \left(b^2-3 a c\right)}{\sqrt{b^2-4 a c}}-a c+b^2\right) \tan ^{-1}\left(\frac{\sqrt{2} \sqrt{c} x}{\sqrt{b-\sqrt{b^2-4 a c}}}\right)}{\sqrt{2} c^{5/2} \sqrt{b-\sqrt{b^2-4 a c}}}+\frac{\left(\frac{b \left(b^2-3 a c\right)}{\sqrt{b^2-4 a c}}-a c+b^2\right) \tan ^{-1}\left(\frac{\sqrt{2} \sqrt{c} x}{\sqrt{\sqrt{b^2-4 a c}+b}}\right)}{\sqrt{2} c^{5/2} \sqrt{\sqrt{b^2-4 a c}+b}}-\frac{b x}{c^2}+\frac{x^3}{3 c}","\frac{\left(-\frac{b \left(b^2-3 a c\right)}{\sqrt{b^2-4 a c}}-a c+b^2\right) \tan ^{-1}\left(\frac{\sqrt{2} \sqrt{c} x}{\sqrt{b-\sqrt{b^2-4 a c}}}\right)}{\sqrt{2} c^{5/2} \sqrt{b-\sqrt{b^2-4 a c}}}+\frac{\left(\frac{b \left(b^2-3 a c\right)}{\sqrt{b^2-4 a c}}-a c+b^2\right) \tan ^{-1}\left(\frac{\sqrt{2} \sqrt{c} x}{\sqrt{\sqrt{b^2-4 a c}+b}}\right)}{\sqrt{2} c^{5/2} \sqrt{\sqrt{b^2-4 a c}+b}}-\frac{b x}{c^2}+\frac{x^3}{3 c}",1,"-((b*x)/c^2) + x^3/(3*c) + ((b^2 - a*c - (b*(b^2 - 3*a*c))/Sqrt[b^2 - 4*a*c])*ArcTan[(Sqrt[2]*Sqrt[c]*x)/Sqrt[b - Sqrt[b^2 - 4*a*c]]])/(Sqrt[2]*c^(5/2)*Sqrt[b - Sqrt[b^2 - 4*a*c]]) + ((b^2 - a*c + (b*(b^2 - 3*a*c))/Sqrt[b^2 - 4*a*c])*ArcTan[(Sqrt[2]*Sqrt[c]*x)/Sqrt[b + Sqrt[b^2 - 4*a*c]]])/(Sqrt[2]*c^(5/2)*Sqrt[b + Sqrt[b^2 - 4*a*c]])","A",6,5,20,0.2500,1,"{1585, 1122, 1279, 1166, 205}"
80,1,81,0,0.0872205,"\int \frac{x^6}{a x+b x^3+c x^5} \, dx","Int[x^6/(a*x + b*x^3 + c*x^5),x]","-\frac{\left(b^2-2 a c\right) \tanh ^{-1}\left(\frac{b+2 c x^2}{\sqrt{b^2-4 a c}}\right)}{2 c^2 \sqrt{b^2-4 a c}}-\frac{b \log \left(a+b x^2+c x^4\right)}{4 c^2}+\frac{x^2}{2 c}","-\frac{\left(b^2-2 a c\right) \tanh ^{-1}\left(\frac{b+2 c x^2}{\sqrt{b^2-4 a c}}\right)}{2 c^2 \sqrt{b^2-4 a c}}-\frac{b \log \left(a+b x^2+c x^4\right)}{4 c^2}+\frac{x^2}{2 c}",1,"x^2/(2*c) - ((b^2 - 2*a*c)*ArcTanh[(b + 2*c*x^2)/Sqrt[b^2 - 4*a*c]])/(2*c^2*Sqrt[b^2 - 4*a*c]) - (b*Log[a + b*x^2 + c*x^4])/(4*c^2)","A",7,7,20,0.3500,1,"{1585, 1114, 703, 634, 618, 206, 628}"
81,1,179,0,0.2273298,"\int \frac{x^5}{a x+b x^3+c x^5} \, dx","Int[x^5/(a*x + b*x^3 + c*x^5),x]","-\frac{\left(b-\frac{b^2-2 a c}{\sqrt{b^2-4 a c}}\right) \tan ^{-1}\left(\frac{\sqrt{2} \sqrt{c} x}{\sqrt{b-\sqrt{b^2-4 a c}}}\right)}{\sqrt{2} c^{3/2} \sqrt{b-\sqrt{b^2-4 a c}}}-\frac{\left(\frac{b^2-2 a c}{\sqrt{b^2-4 a c}}+b\right) \tan ^{-1}\left(\frac{\sqrt{2} \sqrt{c} x}{\sqrt{\sqrt{b^2-4 a c}+b}}\right)}{\sqrt{2} c^{3/2} \sqrt{\sqrt{b^2-4 a c}+b}}+\frac{x}{c}","-\frac{\left(b-\frac{b^2-2 a c}{\sqrt{b^2-4 a c}}\right) \tan ^{-1}\left(\frac{\sqrt{2} \sqrt{c} x}{\sqrt{b-\sqrt{b^2-4 a c}}}\right)}{\sqrt{2} c^{3/2} \sqrt{b-\sqrt{b^2-4 a c}}}-\frac{\left(\frac{b^2-2 a c}{\sqrt{b^2-4 a c}}+b\right) \tan ^{-1}\left(\frac{\sqrt{2} \sqrt{c} x}{\sqrt{\sqrt{b^2-4 a c}+b}}\right)}{\sqrt{2} c^{3/2} \sqrt{\sqrt{b^2-4 a c}+b}}+\frac{x}{c}",1,"x/c - ((b - (b^2 - 2*a*c)/Sqrt[b^2 - 4*a*c])*ArcTan[(Sqrt[2]*Sqrt[c]*x)/Sqrt[b - Sqrt[b^2 - 4*a*c]]])/(Sqrt[2]*c^(3/2)*Sqrt[b - Sqrt[b^2 - 4*a*c]]) - ((b + (b^2 - 2*a*c)/Sqrt[b^2 - 4*a*c])*ArcTan[(Sqrt[2]*Sqrt[c]*x)/Sqrt[b + Sqrt[b^2 - 4*a*c]]])/(Sqrt[2]*c^(3/2)*Sqrt[b + Sqrt[b^2 - 4*a*c]])","A",5,4,20,0.2000,1,"{1585, 1122, 1166, 205}"
82,1,63,0,0.0673125,"\int \frac{x^4}{a x+b x^3+c x^5} \, dx","Int[x^4/(a*x + b*x^3 + c*x^5),x]","\frac{b \tanh ^{-1}\left(\frac{b+2 c x^2}{\sqrt{b^2-4 a c}}\right)}{2 c \sqrt{b^2-4 a c}}+\frac{\log \left(a+b x^2+c x^4\right)}{4 c}","\frac{b \tanh ^{-1}\left(\frac{b+2 c x^2}{\sqrt{b^2-4 a c}}\right)}{2 c \sqrt{b^2-4 a c}}+\frac{\log \left(a+b x^2+c x^4\right)}{4 c}",1,"(b*ArcTanh[(b + 2*c*x^2)/Sqrt[b^2 - 4*a*c]])/(2*c*Sqrt[b^2 - 4*a*c]) + Log[a + b*x^2 + c*x^4]/(4*c)","A",6,6,20,0.3000,1,"{1585, 1114, 634, 618, 206, 628}"
83,1,150,0,0.0937336,"\int \frac{x^3}{a x+b x^3+c x^5} \, dx","Int[x^3/(a*x + b*x^3 + c*x^5),x]","\frac{\sqrt{\sqrt{b^2-4 a c}+b} \tan ^{-1}\left(\frac{\sqrt{2} \sqrt{c} x}{\sqrt{\sqrt{b^2-4 a c}+b}}\right)}{\sqrt{2} \sqrt{c} \sqrt{b^2-4 a c}}-\frac{\sqrt{b-\sqrt{b^2-4 a c}} \tan ^{-1}\left(\frac{\sqrt{2} \sqrt{c} x}{\sqrt{b-\sqrt{b^2-4 a c}}}\right)}{\sqrt{2} \sqrt{c} \sqrt{b^2-4 a c}}","\frac{\sqrt{\sqrt{b^2-4 a c}+b} \tan ^{-1}\left(\frac{\sqrt{2} \sqrt{c} x}{\sqrt{\sqrt{b^2-4 a c}+b}}\right)}{\sqrt{2} \sqrt{c} \sqrt{b^2-4 a c}}-\frac{\sqrt{b-\sqrt{b^2-4 a c}} \tan ^{-1}\left(\frac{\sqrt{2} \sqrt{c} x}{\sqrt{b-\sqrt{b^2-4 a c}}}\right)}{\sqrt{2} \sqrt{c} \sqrt{b^2-4 a c}}",1,"-((Sqrt[b - Sqrt[b^2 - 4*a*c]]*ArcTan[(Sqrt[2]*Sqrt[c]*x)/Sqrt[b - Sqrt[b^2 - 4*a*c]]])/(Sqrt[2]*Sqrt[c]*Sqrt[b^2 - 4*a*c])) + (Sqrt[b + Sqrt[b^2 - 4*a*c]]*ArcTan[(Sqrt[2]*Sqrt[c]*x)/Sqrt[b + Sqrt[b^2 - 4*a*c]]])/(Sqrt[2]*Sqrt[c]*Sqrt[b^2 - 4*a*c])","A",4,3,20,0.1500,1,"{1585, 1130, 205}"
84,1,36,0,0.0426447,"\int \frac{x^2}{a x+b x^3+c x^5} \, dx","Int[x^2/(a*x + b*x^3 + c*x^5),x]","-\frac{\tanh ^{-1}\left(\frac{b+2 c x^2}{\sqrt{b^2-4 a c}}\right)}{\sqrt{b^2-4 a c}}","-\frac{\tanh ^{-1}\left(\frac{b+2 c x^2}{\sqrt{b^2-4 a c}}\right)}{\sqrt{b^2-4 a c}}",1,"-(ArcTanh[(b + 2*c*x^2)/Sqrt[b^2 - 4*a*c]]/Sqrt[b^2 - 4*a*c])","A",4,4,20,0.2000,1,"{1585, 1107, 618, 206}"
85,1,150,0,0.079619,"\int \frac{x}{a x+b x^3+c x^5} \, dx","Int[x/(a*x + b*x^3 + c*x^5),x]","\frac{\sqrt{2} \sqrt{c} \tan ^{-1}\left(\frac{\sqrt{2} \sqrt{c} x}{\sqrt{b-\sqrt{b^2-4 a c}}}\right)}{\sqrt{b^2-4 a c} \sqrt{b-\sqrt{b^2-4 a c}}}-\frac{\sqrt{2} \sqrt{c} \tan ^{-1}\left(\frac{\sqrt{2} \sqrt{c} x}{\sqrt{\sqrt{b^2-4 a c}+b}}\right)}{\sqrt{b^2-4 a c} \sqrt{\sqrt{b^2-4 a c}+b}}","\frac{\sqrt{2} \sqrt{c} \tan ^{-1}\left(\frac{\sqrt{2} \sqrt{c} x}{\sqrt{b-\sqrt{b^2-4 a c}}}\right)}{\sqrt{b^2-4 a c} \sqrt{b-\sqrt{b^2-4 a c}}}-\frac{\sqrt{2} \sqrt{c} \tan ^{-1}\left(\frac{\sqrt{2} \sqrt{c} x}{\sqrt{\sqrt{b^2-4 a c}+b}}\right)}{\sqrt{b^2-4 a c} \sqrt{\sqrt{b^2-4 a c}+b}}",1,"(Sqrt[2]*Sqrt[c]*ArcTan[(Sqrt[2]*Sqrt[c]*x)/Sqrt[b - Sqrt[b^2 - 4*a*c]]])/(Sqrt[b^2 - 4*a*c]*Sqrt[b - Sqrt[b^2 - 4*a*c]]) - (Sqrt[2]*Sqrt[c]*ArcTan[(Sqrt[2]*Sqrt[c]*x)/Sqrt[b + Sqrt[b^2 - 4*a*c]]])/(Sqrt[b^2 - 4*a*c]*Sqrt[b + Sqrt[b^2 - 4*a*c]])","A",4,3,18,0.1667,1,"{1585, 1093, 205}"
86,1,69,0,0.0718082,"\int \frac{1}{a x+b x^3+c x^5} \, dx","Int[(a*x + b*x^3 + c*x^5)^(-1),x]","\frac{b \tanh ^{-1}\left(\frac{b+2 c x^2}{\sqrt{b^2-4 a c}}\right)}{2 a \sqrt{b^2-4 a c}}-\frac{\log \left(a+b x^2+c x^4\right)}{4 a}+\frac{\log (x)}{a}","\frac{b \tanh ^{-1}\left(\frac{b+2 c x^2}{\sqrt{b^2-4 a c}}\right)}{2 a \sqrt{b^2-4 a c}}-\frac{\log \left(a+b x^2+c x^4\right)}{4 a}+\frac{\log (x)}{a}",1,"(b*ArcTanh[(b + 2*c*x^2)/Sqrt[b^2 - 4*a*c]])/(2*a*Sqrt[b^2 - 4*a*c]) + Log[x]/a - Log[a + b*x^2 + c*x^4]/(4*a)","A",8,8,16,0.5000,1,"{1594, 1114, 705, 29, 634, 618, 206, 628}"
87,1,174,0,0.1953194,"\int \frac{1}{x \left(a x+b x^3+c x^5\right)} \, dx","Int[1/(x*(a*x + b*x^3 + c*x^5)),x]","-\frac{\sqrt{c} \left(\frac{b}{\sqrt{b^2-4 a c}}+1\right) \tan ^{-1}\left(\frac{\sqrt{2} \sqrt{c} x}{\sqrt{b-\sqrt{b^2-4 a c}}}\right)}{\sqrt{2} a \sqrt{b-\sqrt{b^2-4 a c}}}-\frac{\sqrt{c} \left(1-\frac{b}{\sqrt{b^2-4 a c}}\right) \tan ^{-1}\left(\frac{\sqrt{2} \sqrt{c} x}{\sqrt{\sqrt{b^2-4 a c}+b}}\right)}{\sqrt{2} a \sqrt{\sqrt{b^2-4 a c}+b}}-\frac{1}{a x}","-\frac{\sqrt{c} \left(\frac{b}{\sqrt{b^2-4 a c}}+1\right) \tan ^{-1}\left(\frac{\sqrt{2} \sqrt{c} x}{\sqrt{b-\sqrt{b^2-4 a c}}}\right)}{\sqrt{2} a \sqrt{b-\sqrt{b^2-4 a c}}}-\frac{\sqrt{c} \left(1-\frac{b}{\sqrt{b^2-4 a c}}\right) \tan ^{-1}\left(\frac{\sqrt{2} \sqrt{c} x}{\sqrt{\sqrt{b^2-4 a c}+b}}\right)}{\sqrt{2} a \sqrt{\sqrt{b^2-4 a c}+b}}-\frac{1}{a x}",1,"-(1/(a*x)) - (Sqrt[c]*(1 + b/Sqrt[b^2 - 4*a*c])*ArcTan[(Sqrt[2]*Sqrt[c]*x)/Sqrt[b - Sqrt[b^2 - 4*a*c]]])/(Sqrt[2]*a*Sqrt[b - Sqrt[b^2 - 4*a*c]]) - (Sqrt[c]*(1 - b/Sqrt[b^2 - 4*a*c])*ArcTan[(Sqrt[2]*Sqrt[c]*x)/Sqrt[b + Sqrt[b^2 - 4*a*c]]])/(Sqrt[2]*a*Sqrt[b + Sqrt[b^2 - 4*a*c]])","A",5,4,20,0.2000,1,"{1585, 1123, 1166, 205}"
88,1,89,0,0.1326957,"\int \frac{1}{x^2 \left(a x+b x^3+c x^5\right)} \, dx","Int[1/(x^2*(a*x + b*x^3 + c*x^5)),x]","-\frac{\left(b^2-2 a c\right) \tanh ^{-1}\left(\frac{b+2 c x^2}{\sqrt{b^2-4 a c}}\right)}{2 a^2 \sqrt{b^2-4 a c}}+\frac{b \log \left(a+b x^2+c x^4\right)}{4 a^2}-\frac{b \log (x)}{a^2}-\frac{1}{2 a x^2}","-\frac{\left(b^2-2 a c\right) \tanh ^{-1}\left(\frac{b+2 c x^2}{\sqrt{b^2-4 a c}}\right)}{2 a^2 \sqrt{b^2-4 a c}}+\frac{b \log \left(a+b x^2+c x^4\right)}{4 a^2}-\frac{b \log (x)}{a^2}-\frac{1}{2 a x^2}",1,"-1/(2*a*x^2) - ((b^2 - 2*a*c)*ArcTanh[(b + 2*c*x^2)/Sqrt[b^2 - 4*a*c]])/(2*a^2*Sqrt[b^2 - 4*a*c]) - (b*Log[x])/a^2 + (b*Log[a + b*x^2 + c*x^4])/(4*a^2)","A",9,8,20,0.4000,1,"{1585, 1114, 709, 800, 634, 618, 206, 628}"
89,1,166,0,0.2226665,"\int \frac{x^{11}}{\left(a x+b x^3+c x^5\right)^2} \, dx","Int[x^11/(a*x + b*x^3 + c*x^5)^2,x]","-\frac{\left(6 a^2 c^2-6 a b^2 c+b^4\right) \tanh ^{-1}\left(\frac{b+2 c x^2}{\sqrt{b^2-4 a c}}\right)}{c^3 \left(b^2-4 a c\right)^{3/2}}+\frac{x^2 \left(b^2-3 a c\right)}{c^2 \left(b^2-4 a c\right)}+\frac{x^6 \left(2 a+b x^2\right)}{2 \left(b^2-4 a c\right) \left(a+b x^2+c x^4\right)}-\frac{b x^4}{2 c \left(b^2-4 a c\right)}-\frac{b \log \left(a+b x^2+c x^4\right)}{2 c^3}","-\frac{\left(6 a^2 c^2-6 a b^2 c+b^4\right) \tanh ^{-1}\left(\frac{b+2 c x^2}{\sqrt{b^2-4 a c}}\right)}{c^3 \left(b^2-4 a c\right)^{3/2}}+\frac{x^2 \left(b^2-3 a c\right)}{c^2 \left(b^2-4 a c\right)}+\frac{x^6 \left(2 a+b x^2\right)}{2 \left(b^2-4 a c\right) \left(a+b x^2+c x^4\right)}-\frac{b x^4}{2 c \left(b^2-4 a c\right)}-\frac{b \log \left(a+b x^2+c x^4\right)}{2 c^3}",1,"((b^2 - 3*a*c)*x^2)/(c^2*(b^2 - 4*a*c)) - (b*x^4)/(2*c*(b^2 - 4*a*c)) + (x^6*(2*a + b*x^2))/(2*(b^2 - 4*a*c)*(a + b*x^2 + c*x^4)) - ((b^4 - 6*a*b^2*c + 6*a^2*c^2)*ArcTanh[(b + 2*c*x^2)/Sqrt[b^2 - 4*a*c]])/(c^3*(b^2 - 4*a*c)^(3/2)) - (b*Log[a + b*x^2 + c*x^4])/(2*c^3)","A",9,8,20,0.4000,1,"{1585, 1114, 738, 800, 634, 618, 206, 628}"
90,1,331,0,0.702875,"\int \frac{x^{10}}{\left(a x+b x^3+c x^5\right)^2} \, dx","Int[x^10/(a*x + b*x^3 + c*x^5)^2,x]","-\frac{\left(-\frac{20 a^2 c^2-19 a b^2 c+3 b^4}{\sqrt{b^2-4 a c}}-13 a b c+3 b^3\right) \tan ^{-1}\left(\frac{\sqrt{2} \sqrt{c} x}{\sqrt{b-\sqrt{b^2-4 a c}}}\right)}{2 \sqrt{2} c^{5/2} \left(b^2-4 a c\right) \sqrt{b-\sqrt{b^2-4 a c}}}-\frac{\left(\frac{20 a^2 c^2-19 a b^2 c+3 b^4}{\sqrt{b^2-4 a c}}-13 a b c+3 b^3\right) \tan ^{-1}\left(\frac{\sqrt{2} \sqrt{c} x}{\sqrt{\sqrt{b^2-4 a c}+b}}\right)}{2 \sqrt{2} c^{5/2} \left(b^2-4 a c\right) \sqrt{\sqrt{b^2-4 a c}+b}}+\frac{x \left(3 b^2-10 a c\right)}{2 c^2 \left(b^2-4 a c\right)}+\frac{x^5 \left(2 a+b x^2\right)}{2 \left(b^2-4 a c\right) \left(a+b x^2+c x^4\right)}-\frac{b x^3}{2 c \left(b^2-4 a c\right)}","-\frac{\left(-\frac{20 a^2 c^2-19 a b^2 c+3 b^4}{\sqrt{b^2-4 a c}}-13 a b c+3 b^3\right) \tan ^{-1}\left(\frac{\sqrt{2} \sqrt{c} x}{\sqrt{b-\sqrt{b^2-4 a c}}}\right)}{2 \sqrt{2} c^{5/2} \left(b^2-4 a c\right) \sqrt{b-\sqrt{b^2-4 a c}}}-\frac{\left(\frac{20 a^2 c^2-19 a b^2 c+3 b^4}{\sqrt{b^2-4 a c}}-13 a b c+3 b^3\right) \tan ^{-1}\left(\frac{\sqrt{2} \sqrt{c} x}{\sqrt{\sqrt{b^2-4 a c}+b}}\right)}{2 \sqrt{2} c^{5/2} \left(b^2-4 a c\right) \sqrt{\sqrt{b^2-4 a c}+b}}+\frac{x \left(3 b^2-10 a c\right)}{2 c^2 \left(b^2-4 a c\right)}+\frac{x^5 \left(2 a+b x^2\right)}{2 \left(b^2-4 a c\right) \left(a+b x^2+c x^4\right)}-\frac{b x^3}{2 c \left(b^2-4 a c\right)}",1,"((3*b^2 - 10*a*c)*x)/(2*c^2*(b^2 - 4*a*c)) - (b*x^3)/(2*c*(b^2 - 4*a*c)) + (x^5*(2*a + b*x^2))/(2*(b^2 - 4*a*c)*(a + b*x^2 + c*x^4)) - ((3*b^3 - 13*a*b*c - (3*b^4 - 19*a*b^2*c + 20*a^2*c^2)/Sqrt[b^2 - 4*a*c])*ArcTan[(Sqrt[2]*Sqrt[c]*x)/Sqrt[b - Sqrt[b^2 - 4*a*c]]])/(2*Sqrt[2]*c^(5/2)*(b^2 - 4*a*c)*Sqrt[b - Sqrt[b^2 - 4*a*c]]) - ((3*b^3 - 13*a*b*c + (3*b^4 - 19*a*b^2*c + 20*a^2*c^2)/Sqrt[b^2 - 4*a*c])*ArcTan[(Sqrt[2]*Sqrt[c]*x)/Sqrt[b + Sqrt[b^2 - 4*a*c]]])/(2*Sqrt[2]*c^(5/2)*(b^2 - 4*a*c)*Sqrt[b + Sqrt[b^2 - 4*a*c]])","A",7,5,20,0.2500,1,"{1585, 1120, 1279, 1166, 205}"
91,1,132,0,0.1517063,"\int \frac{x^9}{\left(a x+b x^3+c x^5\right)^2} \, dx","Int[x^9/(a*x + b*x^3 + c*x^5)^2,x]","\frac{b \left(b^2-6 a c\right) \tanh ^{-1}\left(\frac{b+2 c x^2}{\sqrt{b^2-4 a c}}\right)}{2 c^2 \left(b^2-4 a c\right)^{3/2}}+\frac{x^4 \left(2 a+b x^2\right)}{2 \left(b^2-4 a c\right) \left(a+b x^2+c x^4\right)}-\frac{b x^2}{2 c \left(b^2-4 a c\right)}+\frac{\log \left(a+b x^2+c x^4\right)}{4 c^2}","\frac{b \left(b^2-6 a c\right) \tanh ^{-1}\left(\frac{b+2 c x^2}{\sqrt{b^2-4 a c}}\right)}{2 c^2 \left(b^2-4 a c\right)^{3/2}}+\frac{x^4 \left(2 a+b x^2\right)}{2 \left(b^2-4 a c\right) \left(a+b x^2+c x^4\right)}-\frac{b x^2}{2 c \left(b^2-4 a c\right)}+\frac{\log \left(a+b x^2+c x^4\right)}{4 c^2}",1,"-(b*x^2)/(2*c*(b^2 - 4*a*c)) + (x^4*(2*a + b*x^2))/(2*(b^2 - 4*a*c)*(a + b*x^2 + c*x^4)) + (b*(b^2 - 6*a*c)*ArcTanh[(b + 2*c*x^2)/Sqrt[b^2 - 4*a*c]])/(2*c^2*(b^2 - 4*a*c)^(3/2)) + Log[a + b*x^2 + c*x^4]/(4*c^2)","A",8,8,20,0.4000,1,"{1585, 1114, 738, 773, 634, 618, 206, 628}"
92,1,271,0,0.5255444,"\int \frac{x^8}{\left(a x+b x^3+c x^5\right)^2} \, dx","Int[x^8/(a*x + b*x^3 + c*x^5)^2,x]","\frac{\left(-\frac{b \left(b^2-8 a c\right)}{\sqrt{b^2-4 a c}}-6 a c+b^2\right) \tan ^{-1}\left(\frac{\sqrt{2} \sqrt{c} x}{\sqrt{b-\sqrt{b^2-4 a c}}}\right)}{2 \sqrt{2} c^{3/2} \left(b^2-4 a c\right) \sqrt{b-\sqrt{b^2-4 a c}}}+\frac{\left(\frac{b \left(b^2-8 a c\right)}{\sqrt{b^2-4 a c}}-6 a c+b^2\right) \tan ^{-1}\left(\frac{\sqrt{2} \sqrt{c} x}{\sqrt{\sqrt{b^2-4 a c}+b}}\right)}{2 \sqrt{2} c^{3/2} \left(b^2-4 a c\right) \sqrt{\sqrt{b^2-4 a c}+b}}+\frac{x^3 \left(2 a+b x^2\right)}{2 \left(b^2-4 a c\right) \left(a+b x^2+c x^4\right)}-\frac{b x}{2 c \left(b^2-4 a c\right)}","\frac{\left(-\frac{b \left(b^2-8 a c\right)}{\sqrt{b^2-4 a c}}-6 a c+b^2\right) \tan ^{-1}\left(\frac{\sqrt{2} \sqrt{c} x}{\sqrt{b-\sqrt{b^2-4 a c}}}\right)}{2 \sqrt{2} c^{3/2} \left(b^2-4 a c\right) \sqrt{b-\sqrt{b^2-4 a c}}}+\frac{\left(\frac{b \left(b^2-8 a c\right)}{\sqrt{b^2-4 a c}}-6 a c+b^2\right) \tan ^{-1}\left(\frac{\sqrt{2} \sqrt{c} x}{\sqrt{\sqrt{b^2-4 a c}+b}}\right)}{2 \sqrt{2} c^{3/2} \left(b^2-4 a c\right) \sqrt{\sqrt{b^2-4 a c}+b}}+\frac{x^3 \left(2 a+b x^2\right)}{2 \left(b^2-4 a c\right) \left(a+b x^2+c x^4\right)}-\frac{b x}{2 c \left(b^2-4 a c\right)}",1,"-(b*x)/(2*c*(b^2 - 4*a*c)) + (x^3*(2*a + b*x^2))/(2*(b^2 - 4*a*c)*(a + b*x^2 + c*x^4)) + ((b^2 - 6*a*c - (b*(b^2 - 8*a*c))/Sqrt[b^2 - 4*a*c])*ArcTan[(Sqrt[2]*Sqrt[c]*x)/Sqrt[b - Sqrt[b^2 - 4*a*c]]])/(2*Sqrt[2]*c^(3/2)*(b^2 - 4*a*c)*Sqrt[b - Sqrt[b^2 - 4*a*c]]) + ((b^2 - 6*a*c + (b*(b^2 - 8*a*c))/Sqrt[b^2 - 4*a*c])*ArcTan[(Sqrt[2]*Sqrt[c]*x)/Sqrt[b + Sqrt[b^2 - 4*a*c]]])/(2*Sqrt[2]*c^(3/2)*(b^2 - 4*a*c)*Sqrt[b + Sqrt[b^2 - 4*a*c]])","A",6,5,20,0.2500,1,"{1585, 1120, 1279, 1166, 205}"
93,1,78,0,0.0719037,"\int \frac{x^7}{\left(a x+b x^3+c x^5\right)^2} \, dx","Int[x^7/(a*x + b*x^3 + c*x^5)^2,x]","\frac{x^2 \left(2 a+b x^2\right)}{2 \left(b^2-4 a c\right) \left(a+b x^2+c x^4\right)}+\frac{2 a \tanh ^{-1}\left(\frac{b+2 c x^2}{\sqrt{b^2-4 a c}}\right)}{\left(b^2-4 a c\right)^{3/2}}","\frac{x^2 \left(2 a+b x^2\right)}{2 \left(b^2-4 a c\right) \left(a+b x^2+c x^4\right)}+\frac{2 a \tanh ^{-1}\left(\frac{b+2 c x^2}{\sqrt{b^2-4 a c}}\right)}{\left(b^2-4 a c\right)^{3/2}}",1,"(x^2*(2*a + b*x^2))/(2*(b^2 - 4*a*c)*(a + b*x^2 + c*x^4)) + (2*a*ArcTanh[(b + 2*c*x^2)/Sqrt[b^2 - 4*a*c]])/(b^2 - 4*a*c)^(3/2)","A",5,5,20,0.2500,1,"{1585, 1114, 722, 618, 206}"
94,1,237,0,0.3578262,"\int \frac{x^6}{\left(a x+b x^3+c x^5\right)^2} \, dx","Int[x^6/(a*x + b*x^3 + c*x^5)^2,x]","\frac{x \left(2 a+b x^2\right)}{2 \left(b^2-4 a c\right) \left(a+b x^2+c x^4\right)}+\frac{\left(b-\frac{4 a c+b^2}{\sqrt{b^2-4 a c}}\right) \tan ^{-1}\left(\frac{\sqrt{2} \sqrt{c} x}{\sqrt{b-\sqrt{b^2-4 a c}}}\right)}{2 \sqrt{2} \sqrt{c} \left(b^2-4 a c\right) \sqrt{b-\sqrt{b^2-4 a c}}}+\frac{\left(b \sqrt{b^2-4 a c}+4 a c+b^2\right) \tan ^{-1}\left(\frac{\sqrt{2} \sqrt{c} x}{\sqrt{\sqrt{b^2-4 a c}+b}}\right)}{2 \sqrt{2} \sqrt{c} \left(b^2-4 a c\right)^{3/2} \sqrt{\sqrt{b^2-4 a c}+b}}","\frac{x \left(2 a+b x^2\right)}{2 \left(b^2-4 a c\right) \left(a+b x^2+c x^4\right)}+\frac{\left(b-\frac{4 a c+b^2}{\sqrt{b^2-4 a c}}\right) \tan ^{-1}\left(\frac{\sqrt{2} \sqrt{c} x}{\sqrt{b-\sqrt{b^2-4 a c}}}\right)}{2 \sqrt{2} \sqrt{c} \left(b^2-4 a c\right) \sqrt{b-\sqrt{b^2-4 a c}}}+\frac{\left(b \sqrt{b^2-4 a c}+4 a c+b^2\right) \tan ^{-1}\left(\frac{\sqrt{2} \sqrt{c} x}{\sqrt{\sqrt{b^2-4 a c}+b}}\right)}{2 \sqrt{2} \sqrt{c} \left(b^2-4 a c\right)^{3/2} \sqrt{\sqrt{b^2-4 a c}+b}}",1,"(x*(2*a + b*x^2))/(2*(b^2 - 4*a*c)*(a + b*x^2 + c*x^4)) + ((b - (b^2 + 4*a*c)/Sqrt[b^2 - 4*a*c])*ArcTan[(Sqrt[2]*Sqrt[c]*x)/Sqrt[b - Sqrt[b^2 - 4*a*c]]])/(2*Sqrt[2]*Sqrt[c]*(b^2 - 4*a*c)*Sqrt[b - Sqrt[b^2 - 4*a*c]]) + ((b^2 + 4*a*c + b*Sqrt[b^2 - 4*a*c])*ArcTan[(Sqrt[2]*Sqrt[c]*x)/Sqrt[b + Sqrt[b^2 - 4*a*c]]])/(2*Sqrt[2]*Sqrt[c]*(b^2 - 4*a*c)^(3/2)*Sqrt[b + Sqrt[b^2 - 4*a*c]])","A",5,4,20,0.2000,1,"{1585, 1120, 1166, 205}"
95,1,75,0,0.0689017,"\int \frac{x^5}{\left(a x+b x^3+c x^5\right)^2} \, dx","Int[x^5/(a*x + b*x^3 + c*x^5)^2,x]","\frac{2 a+b x^2}{2 \left(b^2-4 a c\right) \left(a+b x^2+c x^4\right)}-\frac{b \tanh ^{-1}\left(\frac{b+2 c x^2}{\sqrt{b^2-4 a c}}\right)}{\left(b^2-4 a c\right)^{3/2}}","\frac{2 a+b x^2}{2 \left(b^2-4 a c\right) \left(a+b x^2+c x^4\right)}-\frac{b \tanh ^{-1}\left(\frac{b+2 c x^2}{\sqrt{b^2-4 a c}}\right)}{\left(b^2-4 a c\right)^{3/2}}",1,"(2*a + b*x^2)/(2*(b^2 - 4*a*c)*(a + b*x^2 + c*x^4)) - (b*ArcTanh[(b + 2*c*x^2)/Sqrt[b^2 - 4*a*c]])/(b^2 - 4*a*c)^(3/2)","A",5,5,20,0.2500,1,"{1585, 1114, 638, 618, 206}"
96,1,221,0,0.2402465,"\int \frac{x^4}{\left(a x+b x^3+c x^5\right)^2} \, dx","Int[x^4/(a*x + b*x^3 + c*x^5)^2,x]","-\frac{x \left(b+2 c x^2\right)}{2 \left(b^2-4 a c\right) \left(a+b x^2+c x^4\right)}+\frac{\sqrt{c} \left(2 b-\sqrt{b^2-4 a c}\right) \tan ^{-1}\left(\frac{\sqrt{2} \sqrt{c} x}{\sqrt{b-\sqrt{b^2-4 a c}}}\right)}{\sqrt{2} \left(b^2-4 a c\right)^{3/2} \sqrt{b-\sqrt{b^2-4 a c}}}-\frac{\sqrt{c} \left(\sqrt{b^2-4 a c}+2 b\right) \tan ^{-1}\left(\frac{\sqrt{2} \sqrt{c} x}{\sqrt{\sqrt{b^2-4 a c}+b}}\right)}{\sqrt{2} \left(b^2-4 a c\right)^{3/2} \sqrt{\sqrt{b^2-4 a c}+b}}","-\frac{x \left(b+2 c x^2\right)}{2 \left(b^2-4 a c\right) \left(a+b x^2+c x^4\right)}+\frac{\sqrt{c} \left(2 b-\sqrt{b^2-4 a c}\right) \tan ^{-1}\left(\frac{\sqrt{2} \sqrt{c} x}{\sqrt{b-\sqrt{b^2-4 a c}}}\right)}{\sqrt{2} \left(b^2-4 a c\right)^{3/2} \sqrt{b-\sqrt{b^2-4 a c}}}-\frac{\sqrt{c} \left(\sqrt{b^2-4 a c}+2 b\right) \tan ^{-1}\left(\frac{\sqrt{2} \sqrt{c} x}{\sqrt{\sqrt{b^2-4 a c}+b}}\right)}{\sqrt{2} \left(b^2-4 a c\right)^{3/2} \sqrt{\sqrt{b^2-4 a c}+b}}",1,"-(x*(b + 2*c*x^2))/(2*(b^2 - 4*a*c)*(a + b*x^2 + c*x^4)) + (Sqrt[c]*(2*b - Sqrt[b^2 - 4*a*c])*ArcTan[(Sqrt[2]*Sqrt[c]*x)/Sqrt[b - Sqrt[b^2 - 4*a*c]]])/(Sqrt[2]*(b^2 - 4*a*c)^(3/2)*Sqrt[b - Sqrt[b^2 - 4*a*c]]) - (Sqrt[c]*(2*b + Sqrt[b^2 - 4*a*c])*ArcTan[(Sqrt[2]*Sqrt[c]*x)/Sqrt[b + Sqrt[b^2 - 4*a*c]]])/(Sqrt[2]*(b^2 - 4*a*c)^(3/2)*Sqrt[b + Sqrt[b^2 - 4*a*c]])","A",5,4,20,0.2000,1,"{1585, 1119, 1166, 205}"
97,1,74,0,0.0649478,"\int \frac{x^3}{\left(a x+b x^3+c x^5\right)^2} \, dx","Int[x^3/(a*x + b*x^3 + c*x^5)^2,x]","\frac{2 c \tanh ^{-1}\left(\frac{b+2 c x^2}{\sqrt{b^2-4 a c}}\right)}{\left(b^2-4 a c\right)^{3/2}}-\frac{b+2 c x^2}{2 \left(b^2-4 a c\right) \left(a+b x^2+c x^4\right)}","\frac{2 c \tanh ^{-1}\left(\frac{b+2 c x^2}{\sqrt{b^2-4 a c}}\right)}{\left(b^2-4 a c\right)^{3/2}}-\frac{b+2 c x^2}{2 \left(b^2-4 a c\right) \left(a+b x^2+c x^4\right)}",1,"-(b + 2*c*x^2)/(2*(b^2 - 4*a*c)*(a + b*x^2 + c*x^4)) + (2*c*ArcTanh[(b + 2*c*x^2)/Sqrt[b^2 - 4*a*c]])/(b^2 - 4*a*c)^(3/2)","A",5,5,20,0.2500,1,"{1585, 1107, 614, 618, 206}"
98,1,252,0,0.4605602,"\int \frac{x^2}{\left(a x+b x^3+c x^5\right)^2} \, dx","Int[x^2/(a*x + b*x^3 + c*x^5)^2,x]","\frac{x \left(-2 a c+b^2+b c x^2\right)}{2 a \left(b^2-4 a c\right) \left(a+b x^2+c x^4\right)}+\frac{\sqrt{c} \left(b \sqrt{b^2-4 a c}-12 a c+b^2\right) \tan ^{-1}\left(\frac{\sqrt{2} \sqrt{c} x}{\sqrt{b-\sqrt{b^2-4 a c}}}\right)}{2 \sqrt{2} a \left(b^2-4 a c\right)^{3/2} \sqrt{b-\sqrt{b^2-4 a c}}}-\frac{\sqrt{c} \left(-b \sqrt{b^2-4 a c}-12 a c+b^2\right) \tan ^{-1}\left(\frac{\sqrt{2} \sqrt{c} x}{\sqrt{\sqrt{b^2-4 a c}+b}}\right)}{2 \sqrt{2} a \left(b^2-4 a c\right)^{3/2} \sqrt{\sqrt{b^2-4 a c}+b}}","\frac{x \left(-2 a c+b^2+b c x^2\right)}{2 a \left(b^2-4 a c\right) \left(a+b x^2+c x^4\right)}+\frac{\sqrt{c} \left(b \sqrt{b^2-4 a c}-12 a c+b^2\right) \tan ^{-1}\left(\frac{\sqrt{2} \sqrt{c} x}{\sqrt{b-\sqrt{b^2-4 a c}}}\right)}{2 \sqrt{2} a \left(b^2-4 a c\right)^{3/2} \sqrt{b-\sqrt{b^2-4 a c}}}-\frac{\sqrt{c} \left(-b \sqrt{b^2-4 a c}-12 a c+b^2\right) \tan ^{-1}\left(\frac{\sqrt{2} \sqrt{c} x}{\sqrt{\sqrt{b^2-4 a c}+b}}\right)}{2 \sqrt{2} a \left(b^2-4 a c\right)^{3/2} \sqrt{\sqrt{b^2-4 a c}+b}}",1,"(x*(b^2 - 2*a*c + b*c*x^2))/(2*a*(b^2 - 4*a*c)*(a + b*x^2 + c*x^4)) + (Sqrt[c]*(b^2 - 12*a*c + b*Sqrt[b^2 - 4*a*c])*ArcTan[(Sqrt[2]*Sqrt[c]*x)/Sqrt[b - Sqrt[b^2 - 4*a*c]]])/(2*Sqrt[2]*a*(b^2 - 4*a*c)^(3/2)*Sqrt[b - Sqrt[b^2 - 4*a*c]]) - (Sqrt[c]*(b^2 - 12*a*c - b*Sqrt[b^2 - 4*a*c])*ArcTan[(Sqrt[2]*Sqrt[c]*x)/Sqrt[b + Sqrt[b^2 - 4*a*c]]])/(2*Sqrt[2]*a*(b^2 - 4*a*c)^(3/2)*Sqrt[b + Sqrt[b^2 - 4*a*c]])","A",5,4,20,0.2000,1,"{1585, 1092, 1166, 205}"
99,1,122,0,0.1876249,"\int \frac{x}{\left(a x+b x^3+c x^5\right)^2} \, dx","Int[x/(a*x + b*x^3 + c*x^5)^2,x]","\frac{b \left(b^2-6 a c\right) \tanh ^{-1}\left(\frac{b+2 c x^2}{\sqrt{b^2-4 a c}}\right)}{2 a^2 \left(b^2-4 a c\right)^{3/2}}-\frac{\log \left(a+b x^2+c x^4\right)}{4 a^2}+\frac{\log (x)}{a^2}+\frac{-2 a c+b^2+b c x^2}{2 a \left(b^2-4 a c\right) \left(a+b x^2+c x^4\right)}","\frac{b \left(b^2-6 a c\right) \tanh ^{-1}\left(\frac{b+2 c x^2}{\sqrt{b^2-4 a c}}\right)}{2 a^2 \left(b^2-4 a c\right)^{3/2}}-\frac{\log \left(a+b x^2+c x^4\right)}{4 a^2}+\frac{\log (x)}{a^2}+\frac{-2 a c+b^2+b c x^2}{2 a \left(b^2-4 a c\right) \left(a+b x^2+c x^4\right)}",1,"(b^2 - 2*a*c + b*c*x^2)/(2*a*(b^2 - 4*a*c)*(a + b*x^2 + c*x^4)) + (b*(b^2 - 6*a*c)*ArcTanh[(b + 2*c*x^2)/Sqrt[b^2 - 4*a*c]])/(2*a^2*(b^2 - 4*a*c)^(3/2)) + Log[x]/a^2 - Log[a + b*x^2 + c*x^4]/(4*a^2)","A",9,8,18,0.4444,1,"{1585, 1114, 740, 800, 634, 618, 206, 628}"
100,1,308,0,1.3518854,"\int \frac{1}{\left(a x+b x^3+c x^5\right)^2} \, dx","Int[(a*x + b*x^3 + c*x^5)^(-2),x]","-\frac{3 b^2-10 a c}{2 a^2 x \left(b^2-4 a c\right)}-\frac{\sqrt{c} \left(\left(3 b^2-10 a c\right) \sqrt{b^2-4 a c}-16 a b c+3 b^3\right) \tan ^{-1}\left(\frac{\sqrt{2} \sqrt{c} x}{\sqrt{b-\sqrt{b^2-4 a c}}}\right)}{2 \sqrt{2} a^2 \left(b^2-4 a c\right)^{3/2} \sqrt{b-\sqrt{b^2-4 a c}}}+\frac{\sqrt{c} \left(-\left(3 b^2-10 a c\right) \sqrt{b^2-4 a c}-16 a b c+3 b^3\right) \tan ^{-1}\left(\frac{\sqrt{2} \sqrt{c} x}{\sqrt{\sqrt{b^2-4 a c}+b}}\right)}{2 \sqrt{2} a^2 \left(b^2-4 a c\right)^{3/2} \sqrt{\sqrt{b^2-4 a c}+b}}+\frac{-2 a c+b^2+b c x^2}{2 a x \left(b^2-4 a c\right) \left(a+b x^2+c x^4\right)}","-\frac{3 b^2-10 a c}{2 a^2 x \left(b^2-4 a c\right)}-\frac{\sqrt{c} \left(\left(3 b^2-10 a c\right) \sqrt{b^2-4 a c}-16 a b c+3 b^3\right) \tan ^{-1}\left(\frac{\sqrt{2} \sqrt{c} x}{\sqrt{b-\sqrt{b^2-4 a c}}}\right)}{2 \sqrt{2} a^2 \left(b^2-4 a c\right)^{3/2} \sqrt{b-\sqrt{b^2-4 a c}}}+\frac{\sqrt{c} \left(-\left(3 b^2-10 a c\right) \sqrt{b^2-4 a c}-16 a b c+3 b^3\right) \tan ^{-1}\left(\frac{\sqrt{2} \sqrt{c} x}{\sqrt{\sqrt{b^2-4 a c}+b}}\right)}{2 \sqrt{2} a^2 \left(b^2-4 a c\right)^{3/2} \sqrt{\sqrt{b^2-4 a c}+b}}+\frac{-2 a c+b^2+b c x^2}{2 a x \left(b^2-4 a c\right) \left(a+b x^2+c x^4\right)}",1,"-(3*b^2 - 10*a*c)/(2*a^2*(b^2 - 4*a*c)*x) + (b^2 - 2*a*c + b*c*x^2)/(2*a*(b^2 - 4*a*c)*x*(a + b*x^2 + c*x^4)) - (Sqrt[c]*(3*b^3 - 16*a*b*c + (3*b^2 - 10*a*c)*Sqrt[b^2 - 4*a*c])*ArcTan[(Sqrt[2]*Sqrt[c]*x)/Sqrt[b - Sqrt[b^2 - 4*a*c]]])/(2*Sqrt[2]*a^2*(b^2 - 4*a*c)^(3/2)*Sqrt[b - Sqrt[b^2 - 4*a*c]]) + (Sqrt[c]*(3*b^3 - 16*a*b*c - (3*b^2 - 10*a*c)*Sqrt[b^2 - 4*a*c])*ArcTan[(Sqrt[2]*Sqrt[c]*x)/Sqrt[b + Sqrt[b^2 - 4*a*c]]])/(2*Sqrt[2]*a^2*(b^2 - 4*a*c)^(3/2)*Sqrt[b + Sqrt[b^2 - 4*a*c]])","A",6,5,16,0.3125,1,"{1594, 1121, 1281, 1166, 205}"
101,1,162,0,0.2502509,"\int \frac{1}{x \left(a x+b x^3+c x^5\right)^2} \, dx","Int[1/(x*(a*x + b*x^3 + c*x^5)^2),x]","-\frac{\left(6 a^2 c^2-6 a b^2 c+b^4\right) \tanh ^{-1}\left(\frac{b+2 c x^2}{\sqrt{b^2-4 a c}}\right)}{a^3 \left(b^2-4 a c\right)^{3/2}}-\frac{b^2-3 a c}{a^2 x^2 \left(b^2-4 a c\right)}+\frac{b \log \left(a+b x^2+c x^4\right)}{2 a^3}-\frac{2 b \log (x)}{a^3}+\frac{-2 a c+b^2+b c x^2}{2 a x^2 \left(b^2-4 a c\right) \left(a+b x^2+c x^4\right)}","-\frac{\left(6 a^2 c^2-6 a b^2 c+b^4\right) \tanh ^{-1}\left(\frac{b+2 c x^2}{\sqrt{b^2-4 a c}}\right)}{a^3 \left(b^2-4 a c\right)^{3/2}}-\frac{b^2-3 a c}{a^2 x^2 \left(b^2-4 a c\right)}+\frac{b \log \left(a+b x^2+c x^4\right)}{2 a^3}-\frac{2 b \log (x)}{a^3}+\frac{-2 a c+b^2+b c x^2}{2 a x^2 \left(b^2-4 a c\right) \left(a+b x^2+c x^4\right)}",1,"-((b^2 - 3*a*c)/(a^2*(b^2 - 4*a*c)*x^2)) + (b^2 - 2*a*c + b*c*x^2)/(2*a*(b^2 - 4*a*c)*x^2*(a + b*x^2 + c*x^4)) - ((b^4 - 6*a*b^2*c + 6*a^2*c^2)*ArcTanh[(b + 2*c*x^2)/Sqrt[b^2 - 4*a*c]])/(a^3*(b^2 - 4*a*c)^(3/2)) - (2*b*Log[x])/a^3 + (b*Log[a + b*x^2 + c*x^4])/(2*a^3)","A",9,8,20,0.4000,1,"{1585, 1114, 740, 800, 634, 618, 206, 628}"
102,1,361,0,3.077131,"\int \frac{1}{x^2 \left(a x+b x^3+c x^5\right)^2} \, dx","Int[1/(x^2*(a*x + b*x^3 + c*x^5)^2),x]","\frac{\sqrt{c} \left(28 a^2 c^2-29 a b^2 c+b \left(5 b^2-19 a c\right) \sqrt{b^2-4 a c}+5 b^4\right) \tan ^{-1}\left(\frac{\sqrt{2} \sqrt{c} x}{\sqrt{b-\sqrt{b^2-4 a c}}}\right)}{2 \sqrt{2} a^3 \left(b^2-4 a c\right)^{3/2} \sqrt{b-\sqrt{b^2-4 a c}}}-\frac{\sqrt{c} \left(28 a^2 c^2-29 a b^2 c-b \left(5 b^2-19 a c\right) \sqrt{b^2-4 a c}+5 b^4\right) \tan ^{-1}\left(\frac{\sqrt{2} \sqrt{c} x}{\sqrt{\sqrt{b^2-4 a c}+b}}\right)}{2 \sqrt{2} a^3 \left(b^2-4 a c\right)^{3/2} \sqrt{\sqrt{b^2-4 a c}+b}}-\frac{5 b^2-14 a c}{6 a^2 x^3 \left(b^2-4 a c\right)}+\frac{b \left(5 b^2-19 a c\right)}{2 a^3 x \left(b^2-4 a c\right)}+\frac{-2 a c+b^2+b c x^2}{2 a x^3 \left(b^2-4 a c\right) \left(a+b x^2+c x^4\right)}","\frac{\sqrt{c} \left(28 a^2 c^2-29 a b^2 c+b \left(5 b^2-19 a c\right) \sqrt{b^2-4 a c}+5 b^4\right) \tan ^{-1}\left(\frac{\sqrt{2} \sqrt{c} x}{\sqrt{b-\sqrt{b^2-4 a c}}}\right)}{2 \sqrt{2} a^3 \left(b^2-4 a c\right)^{3/2} \sqrt{b-\sqrt{b^2-4 a c}}}-\frac{\sqrt{c} \left(28 a^2 c^2-29 a b^2 c-b \left(5 b^2-19 a c\right) \sqrt{b^2-4 a c}+5 b^4\right) \tan ^{-1}\left(\frac{\sqrt{2} \sqrt{c} x}{\sqrt{\sqrt{b^2-4 a c}+b}}\right)}{2 \sqrt{2} a^3 \left(b^2-4 a c\right)^{3/2} \sqrt{\sqrt{b^2-4 a c}+b}}-\frac{5 b^2-14 a c}{6 a^2 x^3 \left(b^2-4 a c\right)}+\frac{b \left(5 b^2-19 a c\right)}{2 a^3 x \left(b^2-4 a c\right)}+\frac{-2 a c+b^2+b c x^2}{2 a x^3 \left(b^2-4 a c\right) \left(a+b x^2+c x^4\right)}",1,"-(5*b^2 - 14*a*c)/(6*a^2*(b^2 - 4*a*c)*x^3) + (b*(5*b^2 - 19*a*c))/(2*a^3*(b^2 - 4*a*c)*x) + (b^2 - 2*a*c + b*c*x^2)/(2*a*(b^2 - 4*a*c)*x^3*(a + b*x^2 + c*x^4)) + (Sqrt[c]*(5*b^4 - 29*a*b^2*c + 28*a^2*c^2 + b*(5*b^2 - 19*a*c)*Sqrt[b^2 - 4*a*c])*ArcTan[(Sqrt[2]*Sqrt[c]*x)/Sqrt[b - Sqrt[b^2 - 4*a*c]]])/(2*Sqrt[2]*a^3*(b^2 - 4*a*c)^(3/2)*Sqrt[b - Sqrt[b^2 - 4*a*c]]) - (Sqrt[c]*(5*b^4 - 29*a*b^2*c + 28*a^2*c^2 - b*(5*b^2 - 19*a*c)*Sqrt[b^2 - 4*a*c])*ArcTan[(Sqrt[2]*Sqrt[c]*x)/Sqrt[b + Sqrt[b^2 - 4*a*c]]])/(2*Sqrt[2]*a^3*(b^2 - 4*a*c)^(3/2)*Sqrt[b + Sqrt[b^2 - 4*a*c]])","A",7,5,20,0.2500,1,"{1585, 1121, 1281, 1166, 205}"
103,1,219,0,0.3124607,"\int \frac{1}{x^3 \left(a x+b x^3+c x^5\right)^2} \, dx","Int[1/(x^3*(a*x + b*x^3 + c*x^5)^2),x]","\frac{b \left(30 a^2 c^2-20 a b^2 c+3 b^4\right) \tanh ^{-1}\left(\frac{b+2 c x^2}{\sqrt{b^2-4 a c}}\right)}{2 a^4 \left(b^2-4 a c\right)^{3/2}}+\frac{b \left(3 b^2-11 a c\right)}{2 a^3 x^2 \left(b^2-4 a c\right)}-\frac{3 b^2-8 a c}{4 a^2 x^4 \left(b^2-4 a c\right)}-\frac{\left(3 b^2-2 a c\right) \log \left(a+b x^2+c x^4\right)}{4 a^4}+\frac{\log (x) \left(3 b^2-2 a c\right)}{a^4}+\frac{-2 a c+b^2+b c x^2}{2 a x^4 \left(b^2-4 a c\right) \left(a+b x^2+c x^4\right)}","\frac{b \left(30 a^2 c^2-20 a b^2 c+3 b^4\right) \tanh ^{-1}\left(\frac{b+2 c x^2}{\sqrt{b^2-4 a c}}\right)}{2 a^4 \left(b^2-4 a c\right)^{3/2}}+\frac{b \left(3 b^2-11 a c\right)}{2 a^3 x^2 \left(b^2-4 a c\right)}-\frac{3 b^2-8 a c}{4 a^2 x^4 \left(b^2-4 a c\right)}-\frac{\left(3 b^2-2 a c\right) \log \left(a+b x^2+c x^4\right)}{4 a^4}+\frac{\log (x) \left(3 b^2-2 a c\right)}{a^4}+\frac{-2 a c+b^2+b c x^2}{2 a x^4 \left(b^2-4 a c\right) \left(a+b x^2+c x^4\right)}",1,"-(3*b^2 - 8*a*c)/(4*a^2*(b^2 - 4*a*c)*x^4) + (b*(3*b^2 - 11*a*c))/(2*a^3*(b^2 - 4*a*c)*x^2) + (b^2 - 2*a*c + b*c*x^2)/(2*a*(b^2 - 4*a*c)*x^4*(a + b*x^2 + c*x^4)) + (b*(3*b^4 - 20*a*b^2*c + 30*a^2*c^2)*ArcTanh[(b + 2*c*x^2)/Sqrt[b^2 - 4*a*c]])/(2*a^4*(b^2 - 4*a*c)^(3/2)) + ((3*b^2 - 2*a*c)*Log[x])/a^4 - ((3*b^2 - 2*a*c)*Log[a + b*x^2 + c*x^4])/(4*a^4)","A",9,8,20,0.4000,1,"{1585, 1114, 740, 800, 634, 618, 206, 628}"
104,1,142,0,0.1708306,"\int \frac{x}{\sqrt{a x+b x^3+c x^5}} \, dx","Int[x/Sqrt[a*x + b*x^3 + c*x^5],x]","\frac{2 x^2 \sqrt{\frac{2 c x^2}{b-\sqrt{b^2-4 a c}}+1} \sqrt{\frac{2 c x^2}{\sqrt{b^2-4 a c}+b}+1} F_1\left(\frac{3}{4};\frac{1}{2},\frac{1}{2};\frac{7}{4};-\frac{2 c x^2}{b-\sqrt{b^2-4 a c}},-\frac{2 c x^2}{b+\sqrt{b^2-4 a c}}\right)}{3 \sqrt{a x+b x^3+c x^5}}","\frac{2 x^2 \sqrt{\frac{2 c x^2}{b-\sqrt{b^2-4 a c}}+1} \sqrt{\frac{2 c x^2}{\sqrt{b^2-4 a c}+b}+1} F_1\left(\frac{3}{4};\frac{1}{2},\frac{1}{2};\frac{7}{4};-\frac{2 c x^2}{b-\sqrt{b^2-4 a c}},-\frac{2 c x^2}{b+\sqrt{b^2-4 a c}}\right)}{3 \sqrt{a x+b x^3+c x^5}}",1,"(2*x^2*Sqrt[1 + (2*c*x^2)/(b - Sqrt[b^2 - 4*a*c])]*Sqrt[1 + (2*c*x^2)/(b + Sqrt[b^2 - 4*a*c])]*AppellF1[3/4, 1/2, 1/2, 7/4, (-2*c*x^2)/(b - Sqrt[b^2 - 4*a*c]), (-2*c*x^2)/(b + Sqrt[b^2 - 4*a*c])])/(3*Sqrt[a*x + b*x^3 + c*x^5])","A",3,3,20,0.1500,1,"{1930, 1141, 510}"
105,1,380,0,0.2873449,"\int x^{3/2} \sqrt{a x+b x^3+c x^5} \, dx","Int[x^(3/2)*Sqrt[a*x + b*x^3 + c*x^5],x]","-\frac{2 x^{3/2} \left(b^2-3 a c\right) \left(a+b x^2+c x^4\right)}{15 c^{3/2} \left(\sqrt{a}+\sqrt{c} x^2\right) \sqrt{a x+b x^3+c x^5}}-\frac{\sqrt[4]{a} \sqrt{x} \left(\sqrt{a} b \sqrt{c}-6 a c+2 b^2\right) \left(\sqrt{a}+\sqrt{c} x^2\right) \sqrt{\frac{a+b x^2+c x^4}{\left(\sqrt{a}+\sqrt{c} x^2\right)^2}} F\left(2 \tan ^{-1}\left(\frac{\sqrt[4]{c} x}{\sqrt[4]{a}}\right)|\frac{1}{4} \left(2-\frac{b}{\sqrt{a} \sqrt{c}}\right)\right)}{30 c^{7/4} \sqrt{a x+b x^3+c x^5}}+\frac{2 \sqrt[4]{a} \sqrt{x} \left(b^2-3 a c\right) \left(\sqrt{a}+\sqrt{c} x^2\right) \sqrt{\frac{a+b x^2+c x^4}{\left(\sqrt{a}+\sqrt{c} x^2\right)^2}} E\left(2 \tan ^{-1}\left(\frac{\sqrt[4]{c} x}{\sqrt[4]{a}}\right)|\frac{1}{4} \left(2-\frac{b}{\sqrt{a} \sqrt{c}}\right)\right)}{15 c^{7/4} \sqrt{a x+b x^3+c x^5}}+\frac{\sqrt{x} \left(b+3 c x^2\right) \sqrt{a x+b x^3+c x^5}}{15 c}","-\frac{2 x^{3/2} \left(b^2-3 a c\right) \left(a+b x^2+c x^4\right)}{15 c^{3/2} \left(\sqrt{a}+\sqrt{c} x^2\right) \sqrt{a x+b x^3+c x^5}}-\frac{\sqrt[4]{a} \sqrt{x} \left(\sqrt{a} b \sqrt{c}-6 a c+2 b^2\right) \left(\sqrt{a}+\sqrt{c} x^2\right) \sqrt{\frac{a+b x^2+c x^4}{\left(\sqrt{a}+\sqrt{c} x^2\right)^2}} F\left(2 \tan ^{-1}\left(\frac{\sqrt[4]{c} x}{\sqrt[4]{a}}\right)|\frac{1}{4} \left(2-\frac{b}{\sqrt{a} \sqrt{c}}\right)\right)}{30 c^{7/4} \sqrt{a x+b x^3+c x^5}}+\frac{2 \sqrt[4]{a} \sqrt{x} \left(b^2-3 a c\right) \left(\sqrt{a}+\sqrt{c} x^2\right) \sqrt{\frac{a+b x^2+c x^4}{\left(\sqrt{a}+\sqrt{c} x^2\right)^2}} E\left(2 \tan ^{-1}\left(\frac{\sqrt[4]{c} x}{\sqrt[4]{a}}\right)|\frac{1}{4} \left(2-\frac{b}{\sqrt{a} \sqrt{c}}\right)\right)}{15 c^{7/4} \sqrt{a x+b x^3+c x^5}}+\frac{\sqrt{x} \left(b+3 c x^2\right) \sqrt{a x+b x^3+c x^5}}{15 c}",1,"(-2*(b^2 - 3*a*c)*x^(3/2)*(a + b*x^2 + c*x^4))/(15*c^(3/2)*(Sqrt[a] + Sqrt[c]*x^2)*Sqrt[a*x + b*x^3 + c*x^5]) + (Sqrt[x]*(b + 3*c*x^2)*Sqrt[a*x + b*x^3 + c*x^5])/(15*c) + (2*a^(1/4)*(b^2 - 3*a*c)*Sqrt[x]*(Sqrt[a] + Sqrt[c]*x^2)*Sqrt[(a + b*x^2 + c*x^4)/(Sqrt[a] + Sqrt[c]*x^2)^2]*EllipticE[2*ArcTan[(c^(1/4)*x)/a^(1/4)], (2 - b/(Sqrt[a]*Sqrt[c]))/4])/(15*c^(7/4)*Sqrt[a*x + b*x^3 + c*x^5]) - (a^(1/4)*(2*b^2 + Sqrt[a]*b*Sqrt[c] - 6*a*c)*Sqrt[x]*(Sqrt[a] + Sqrt[c]*x^2)*Sqrt[(a + b*x^2 + c*x^4)/(Sqrt[a] + Sqrt[c]*x^2)^2]*EllipticF[2*ArcTan[(c^(1/4)*x)/a^(1/4)], (2 - b/(Sqrt[a]*Sqrt[c]))/4])/(30*c^(7/4)*Sqrt[a*x + b*x^3 + c*x^5])","A",5,5,24,0.2083,1,"{1919, 1953, 1197, 1103, 1195}"
106,1,129,0,0.0933199,"\int \sqrt{x} \sqrt{a x+b x^3+c x^5} \, dx","Int[Sqrt[x]*Sqrt[a*x + b*x^3 + c*x^5],x]","\frac{\left(b+2 c x^2\right) \sqrt{a x+b x^3+c x^5}}{8 c \sqrt{x}}-\frac{\sqrt{x} \left(b^2-4 a c\right) \sqrt{a+b x^2+c x^4} \tanh ^{-1}\left(\frac{b+2 c x^2}{2 \sqrt{c} \sqrt{a+b x^2+c x^4}}\right)}{16 c^{3/2} \sqrt{a x+b x^3+c x^5}}","\frac{\left(b+2 c x^2\right) \sqrt{a x+b x^3+c x^5}}{8 c \sqrt{x}}-\frac{\sqrt{x} \left(b^2-4 a c\right) \sqrt{a+b x^2+c x^4} \tanh ^{-1}\left(\frac{b+2 c x^2}{2 \sqrt{c} \sqrt{a+b x^2+c x^4}}\right)}{16 c^{3/2} \sqrt{a x+b x^3+c x^5}}",1,"((b + 2*c*x^2)*Sqrt[a*x + b*x^3 + c*x^5])/(8*c*Sqrt[x]) - ((b^2 - 4*a*c)*Sqrt[x]*Sqrt[a + b*x^2 + c*x^4]*ArcTanh[(b + 2*c*x^2)/(2*Sqrt[c]*Sqrt[a + b*x^2 + c*x^4])])/(16*c^(3/2)*Sqrt[a*x + b*x^3 + c*x^5])","A",5,5,24,0.2083,1,"{1918, 1914, 1107, 621, 206}"
107,1,347,0,0.2244181,"\int \frac{\sqrt{a x+b x^3+c x^5}}{\sqrt{x}} \, dx","Int[Sqrt[a*x + b*x^3 + c*x^5]/Sqrt[x],x]","\frac{\sqrt[4]{a} \sqrt{x} \left(2 \sqrt{a} \sqrt{c}+b\right) \left(\sqrt{a}+\sqrt{c} x^2\right) \sqrt{\frac{a+b x^2+c x^4}{\left(\sqrt{a}+\sqrt{c} x^2\right)^2}} F\left(2 \tan ^{-1}\left(\frac{\sqrt[4]{c} x}{\sqrt[4]{a}}\right)|\frac{1}{4} \left(2-\frac{b}{\sqrt{a} \sqrt{c}}\right)\right)}{6 c^{3/4} \sqrt{a x+b x^3+c x^5}}-\frac{\sqrt[4]{a} b \sqrt{x} \left(\sqrt{a}+\sqrt{c} x^2\right) \sqrt{\frac{a+b x^2+c x^4}{\left(\sqrt{a}+\sqrt{c} x^2\right)^2}} E\left(2 \tan ^{-1}\left(\frac{\sqrt[4]{c} x}{\sqrt[4]{a}}\right)|\frac{1}{4} \left(2-\frac{b}{\sqrt{a} \sqrt{c}}\right)\right)}{3 c^{3/4} \sqrt{a x+b x^3+c x^5}}+\frac{b x^{3/2} \left(a+b x^2+c x^4\right)}{3 \sqrt{c} \left(\sqrt{a}+\sqrt{c} x^2\right) \sqrt{a x+b x^3+c x^5}}+\frac{1}{3} \sqrt{x} \sqrt{a x+b x^3+c x^5}","\frac{\sqrt[4]{a} \sqrt{x} \left(2 \sqrt{a} \sqrt{c}+b\right) \left(\sqrt{a}+\sqrt{c} x^2\right) \sqrt{\frac{a+b x^2+c x^4}{\left(\sqrt{a}+\sqrt{c} x^2\right)^2}} F\left(2 \tan ^{-1}\left(\frac{\sqrt[4]{c} x}{\sqrt[4]{a}}\right)|\frac{1}{4} \left(2-\frac{b}{\sqrt{a} \sqrt{c}}\right)\right)}{6 c^{3/4} \sqrt{a x+b x^3+c x^5}}-\frac{\sqrt[4]{a} b \sqrt{x} \left(\sqrt{a}+\sqrt{c} x^2\right) \sqrt{\frac{a+b x^2+c x^4}{\left(\sqrt{a}+\sqrt{c} x^2\right)^2}} E\left(2 \tan ^{-1}\left(\frac{\sqrt[4]{c} x}{\sqrt[4]{a}}\right)|\frac{1}{4} \left(2-\frac{b}{\sqrt{a} \sqrt{c}}\right)\right)}{3 c^{3/4} \sqrt{a x+b x^3+c x^5}}+\frac{b x^{3/2} \left(a+b x^2+c x^4\right)}{3 \sqrt{c} \left(\sqrt{a}+\sqrt{c} x^2\right) \sqrt{a x+b x^3+c x^5}}+\frac{1}{3} \sqrt{x} \sqrt{a x+b x^3+c x^5}",1,"(b*x^(3/2)*(a + b*x^2 + c*x^4))/(3*Sqrt[c]*(Sqrt[a] + Sqrt[c]*x^2)*Sqrt[a*x + b*x^3 + c*x^5]) + (Sqrt[x]*Sqrt[a*x + b*x^3 + c*x^5])/3 - (a^(1/4)*b*Sqrt[x]*(Sqrt[a] + Sqrt[c]*x^2)*Sqrt[(a + b*x^2 + c*x^4)/(Sqrt[a] + Sqrt[c]*x^2)^2]*EllipticE[2*ArcTan[(c^(1/4)*x)/a^(1/4)], (2 - b/(Sqrt[a]*Sqrt[c]))/4])/(3*c^(3/4)*Sqrt[a*x + b*x^3 + c*x^5]) + (a^(1/4)*(b + 2*Sqrt[a]*Sqrt[c])*Sqrt[x]*(Sqrt[a] + Sqrt[c]*x^2)*Sqrt[(a + b*x^2 + c*x^4)/(Sqrt[a] + Sqrt[c]*x^2)^2]*EllipticF[2*ArcTan[(c^(1/4)*x)/a^(1/4)], (2 - b/(Sqrt[a]*Sqrt[c]))/4])/(6*c^(3/4)*Sqrt[a*x + b*x^3 + c*x^5])","A",5,5,24,0.2083,1,"{1921, 1953, 1197, 1103, 1195}"
108,1,194,0,0.2089639,"\int \frac{\sqrt{a x+b x^3+c x^5}}{x^{3/2}} \, dx","Int[Sqrt[a*x + b*x^3 + c*x^5]/x^(3/2),x]","\frac{\sqrt{a x+b x^3+c x^5}}{2 \sqrt{x}}-\frac{\sqrt{a} \sqrt{x} \sqrt{a+b x^2+c x^4} \tanh ^{-1}\left(\frac{2 a+b x^2}{2 \sqrt{a} \sqrt{a+b x^2+c x^4}}\right)}{2 \sqrt{a x+b x^3+c x^5}}+\frac{b \sqrt{x} \sqrt{a+b x^2+c x^4} \tanh ^{-1}\left(\frac{b+2 c x^2}{2 \sqrt{c} \sqrt{a+b x^2+c x^4}}\right)}{4 \sqrt{c} \sqrt{a x+b x^3+c x^5}}","\frac{\sqrt{a x+b x^3+c x^5}}{2 \sqrt{x}}-\frac{\sqrt{a} \sqrt{x} \sqrt{a+b x^2+c x^4} \tanh ^{-1}\left(\frac{2 a+b x^2}{2 \sqrt{a} \sqrt{a+b x^2+c x^4}}\right)}{2 \sqrt{a x+b x^3+c x^5}}+\frac{b \sqrt{x} \sqrt{a+b x^2+c x^4} \tanh ^{-1}\left(\frac{b+2 c x^2}{2 \sqrt{c} \sqrt{a+b x^2+c x^4}}\right)}{4 \sqrt{c} \sqrt{a x+b x^3+c x^5}}",1,"Sqrt[a*x + b*x^3 + c*x^5]/(2*Sqrt[x]) - (Sqrt[a]*Sqrt[x]*Sqrt[a + b*x^2 + c*x^4]*ArcTanh[(2*a + b*x^2)/(2*Sqrt[a]*Sqrt[a + b*x^2 + c*x^4])])/(2*Sqrt[a*x + b*x^3 + c*x^5]) + (b*Sqrt[x]*Sqrt[a + b*x^2 + c*x^4]*ArcTanh[(b + 2*c*x^2)/(2*Sqrt[c]*Sqrt[a + b*x^2 + c*x^4])])/(4*Sqrt[c]*Sqrt[a*x + b*x^3 + c*x^5])","A",8,7,24,0.2917,1,"{1921, 1953, 1251, 843, 621, 206, 724}"
109,1,244,0,0.3572059,"\int x^{3/2} \left(a x+b x^3+c x^5\right)^{3/2} \, dx","Int[x^(3/2)*(a*x + b*x^3 + c*x^5)^(3/2),x]","\frac{\left(128 a^2 c^2-100 a b^2 c+15 b^4\right) \sqrt{a x+b x^3+c x^5}}{1280 c^3 \sqrt{x}}-\frac{x^{3/2} \left(4 c x^2 \left(5 b^2-16 a c\right)+b \left(5 b^2-4 a c\right)\right) \sqrt{a x+b x^3+c x^5}}{640 c^2}-\frac{3 b \sqrt{x} \left(b^2-4 a c\right)^2 \sqrt{a+b x^2+c x^4} \tanh ^{-1}\left(\frac{b+2 c x^2}{2 \sqrt{c} \sqrt{a+b x^2+c x^4}}\right)}{512 c^{7/2} \sqrt{a x+b x^3+c x^5}}+\frac{\sqrt{x} \left(3 b+8 c x^2\right) \left(a x+b x^3+c x^5\right)^{3/2}}{80 c}","\frac{\left(128 a^2 c^2-100 a b^2 c+15 b^4\right) \sqrt{a x+b x^3+c x^5}}{1280 c^3 \sqrt{x}}-\frac{x^{3/2} \left(4 c x^2 \left(5 b^2-16 a c\right)+b \left(5 b^2-4 a c\right)\right) \sqrt{a x+b x^3+c x^5}}{640 c^2}-\frac{3 b \sqrt{x} \left(b^2-4 a c\right)^2 \sqrt{a+b x^2+c x^4} \tanh ^{-1}\left(\frac{b+2 c x^2}{2 \sqrt{c} \sqrt{a+b x^2+c x^4}}\right)}{512 c^{7/2} \sqrt{a x+b x^3+c x^5}}+\frac{\sqrt{x} \left(3 b+8 c x^2\right) \left(a x+b x^3+c x^5\right)^{3/2}}{80 c}",1,"((15*b^4 - 100*a*b^2*c + 128*a^2*c^2)*Sqrt[a*x + b*x^3 + c*x^5])/(1280*c^3*Sqrt[x]) - (x^(3/2)*(b*(5*b^2 - 4*a*c) + 4*c*(5*b^2 - 16*a*c)*x^2)*Sqrt[a*x + b*x^3 + c*x^5])/(640*c^2) + (Sqrt[x]*(3*b + 8*c*x^2)*(a*x + b*x^3 + c*x^5)^(3/2))/(80*c) - (3*b*(b^2 - 4*a*c)^2*Sqrt[x]*Sqrt[a + b*x^2 + c*x^4]*ArcTanh[(b + 2*c*x^2)/(2*Sqrt[c]*Sqrt[a + b*x^2 + c*x^4])])/(512*c^(7/2)*Sqrt[a*x + b*x^3 + c*x^5])","A",8,8,24,0.3333,1,"{1919, 1945, 1949, 12, 1914, 1107, 621, 206}"
110,1,487,0,0.4570438,"\int \sqrt{x} \left(a x+b x^3+c x^5\right)^{3/2} \, dx","Int[Sqrt[x]*(a*x + b*x^3 + c*x^5)^(3/2),x]","\frac{x^{3/2} \left(84 a^2 c^2-57 a b^2 c+8 b^4\right) \left(a+b x^2+c x^4\right)}{315 c^{5/2} \left(\sqrt{a}+\sqrt{c} x^2\right) \sqrt{a x+b x^3+c x^5}}+\frac{\sqrt[4]{a} \sqrt{x} \left(84 a^2 c^2-57 a b^2 c+4 \sqrt{a} b \sqrt{c} \left(b^2-6 a c\right)+8 b^4\right) \left(\sqrt{a}+\sqrt{c} x^2\right) \sqrt{\frac{a+b x^2+c x^4}{\left(\sqrt{a}+\sqrt{c} x^2\right)^2}} F\left(2 \tan ^{-1}\left(\frac{\sqrt[4]{c} x}{\sqrt[4]{a}}\right)|\frac{1}{4} \left(2-\frac{b}{\sqrt{a} \sqrt{c}}\right)\right)}{630 c^{11/4} \sqrt{a x+b x^3+c x^5}}-\frac{\sqrt[4]{a} \sqrt{x} \left(84 a^2 c^2-57 a b^2 c+8 b^4\right) \left(\sqrt{a}+\sqrt{c} x^2\right) \sqrt{\frac{a+b x^2+c x^4}{\left(\sqrt{a}+\sqrt{c} x^2\right)^2}} E\left(2 \tan ^{-1}\left(\frac{\sqrt[4]{c} x}{\sqrt[4]{a}}\right)|\frac{1}{4} \left(2-\frac{b}{\sqrt{a} \sqrt{c}}\right)\right)}{315 c^{11/4} \sqrt{a x+b x^3+c x^5}}-\frac{\sqrt{x} \left(6 c x^2 \left(2 b^2-7 a c\right)+b \left(4 b^2-9 a c\right)\right) \sqrt{a x+b x^3+c x^5}}{315 c^2}+\frac{\left(3 b+7 c x^2\right) \left(a x+b x^3+c x^5\right)^{3/2}}{63 c \sqrt{x}}","\frac{x^{3/2} \left(84 a^2 c^2-57 a b^2 c+8 b^4\right) \left(a+b x^2+c x^4\right)}{315 c^{5/2} \left(\sqrt{a}+\sqrt{c} x^2\right) \sqrt{a x+b x^3+c x^5}}+\frac{\sqrt[4]{a} \sqrt{x} \left(84 a^2 c^2-57 a b^2 c+4 \sqrt{a} b \sqrt{c} \left(b^2-6 a c\right)+8 b^4\right) \left(\sqrt{a}+\sqrt{c} x^2\right) \sqrt{\frac{a+b x^2+c x^4}{\left(\sqrt{a}+\sqrt{c} x^2\right)^2}} F\left(2 \tan ^{-1}\left(\frac{\sqrt[4]{c} x}{\sqrt[4]{a}}\right)|\frac{1}{4} \left(2-\frac{b}{\sqrt{a} \sqrt{c}}\right)\right)}{630 c^{11/4} \sqrt{a x+b x^3+c x^5}}-\frac{\sqrt[4]{a} \sqrt{x} \left(84 a^2 c^2-57 a b^2 c+8 b^4\right) \left(\sqrt{a}+\sqrt{c} x^2\right) \sqrt{\frac{a+b x^2+c x^4}{\left(\sqrt{a}+\sqrt{c} x^2\right)^2}} E\left(2 \tan ^{-1}\left(\frac{\sqrt[4]{c} x}{\sqrt[4]{a}}\right)|\frac{1}{4} \left(2-\frac{b}{\sqrt{a} \sqrt{c}}\right)\right)}{315 c^{11/4} \sqrt{a x+b x^3+c x^5}}-\frac{\sqrt{x} \left(6 c x^2 \left(2 b^2-7 a c\right)+b \left(4 b^2-9 a c\right)\right) \sqrt{a x+b x^3+c x^5}}{315 c^2}+\frac{\left(3 b+7 c x^2\right) \left(a x+b x^3+c x^5\right)^{3/2}}{63 c \sqrt{x}}",1,"((8*b^4 - 57*a*b^2*c + 84*a^2*c^2)*x^(3/2)*(a + b*x^2 + c*x^4))/(315*c^(5/2)*(Sqrt[a] + Sqrt[c]*x^2)*Sqrt[a*x + b*x^3 + c*x^5]) - (Sqrt[x]*(b*(4*b^2 - 9*a*c) + 6*c*(2*b^2 - 7*a*c)*x^2)*Sqrt[a*x + b*x^3 + c*x^5])/(315*c^2) + ((3*b + 7*c*x^2)*(a*x + b*x^3 + c*x^5)^(3/2))/(63*c*Sqrt[x]) - (a^(1/4)*(8*b^4 - 57*a*b^2*c + 84*a^2*c^2)*Sqrt[x]*(Sqrt[a] + Sqrt[c]*x^2)*Sqrt[(a + b*x^2 + c*x^4)/(Sqrt[a] + Sqrt[c]*x^2)^2]*EllipticE[2*ArcTan[(c^(1/4)*x)/a^(1/4)], (2 - b/(Sqrt[a]*Sqrt[c]))/4])/(315*c^(11/4)*Sqrt[a*x + b*x^3 + c*x^5]) + (a^(1/4)*(8*b^4 - 57*a*b^2*c + 84*a^2*c^2 + 4*Sqrt[a]*b*Sqrt[c]*(b^2 - 6*a*c))*Sqrt[x]*(Sqrt[a] + Sqrt[c]*x^2)*Sqrt[(a + b*x^2 + c*x^4)/(Sqrt[a] + Sqrt[c]*x^2)^2]*EllipticF[2*ArcTan[(c^(1/4)*x)/a^(1/4)], (2 - b/(Sqrt[a]*Sqrt[c]))/4])/(630*c^(11/4)*Sqrt[a*x + b*x^3 + c*x^5])","A",6,6,24,0.2500,1,"{1919, 1945, 1953, 1197, 1103, 1195}"
111,1,177,0,0.1383444,"\int \frac{\left(a x+b x^3+c x^5\right)^{3/2}}{\sqrt{x}} \, dx","Int[(a*x + b*x^3 + c*x^5)^(3/2)/Sqrt[x],x]","-\frac{3 \left(b^2-4 a c\right) \left(b+2 c x^2\right) \sqrt{a x+b x^3+c x^5}}{128 c^2 \sqrt{x}}+\frac{3 \sqrt{x} \left(b^2-4 a c\right)^2 \sqrt{a+b x^2+c x^4} \tanh ^{-1}\left(\frac{b+2 c x^2}{2 \sqrt{c} \sqrt{a+b x^2+c x^4}}\right)}{256 c^{5/2} \sqrt{a x+b x^3+c x^5}}+\frac{\left(b+2 c x^2\right) \left(a x+b x^3+c x^5\right)^{3/2}}{16 c x^{3/2}}","-\frac{3 \left(b^2-4 a c\right) \left(b+2 c x^2\right) \sqrt{a x+b x^3+c x^5}}{128 c^2 \sqrt{x}}+\frac{3 \sqrt{x} \left(b^2-4 a c\right)^2 \sqrt{a+b x^2+c x^4} \tanh ^{-1}\left(\frac{b+2 c x^2}{2 \sqrt{c} \sqrt{a+b x^2+c x^4}}\right)}{256 c^{5/2} \sqrt{a x+b x^3+c x^5}}+\frac{\left(b+2 c x^2\right) \left(a x+b x^3+c x^5\right)^{3/2}}{16 c x^{3/2}}",1,"(-3*(b^2 - 4*a*c)*(b + 2*c*x^2)*Sqrt[a*x + b*x^3 + c*x^5])/(128*c^2*Sqrt[x]) + ((b + 2*c*x^2)*(a*x + b*x^3 + c*x^5)^(3/2))/(16*c*x^(3/2)) + (3*(b^2 - 4*a*c)^2*Sqrt[x]*Sqrt[a + b*x^2 + c*x^4]*ArcTanh[(b + 2*c*x^2)/(2*Sqrt[c]*Sqrt[a + b*x^2 + c*x^4])])/(256*c^(5/2)*Sqrt[a*x + b*x^3 + c*x^5])","A",6,5,24,0.2083,1,"{1918, 1914, 1107, 621, 206}"
112,1,425,0,0.4485504,"\int \frac{\left(a x+b x^3+c x^5\right)^{3/2}}{x^{3/2}} \, dx","Int[(a*x + b*x^3 + c*x^5)^(3/2)/x^(3/2),x]","-\frac{2 b x^{3/2} \left(b^2-8 a c\right) \left(a+b x^2+c x^4\right)}{35 c^{3/2} \left(\sqrt{a}+\sqrt{c} x^2\right) \sqrt{a x+b x^3+c x^5}}-\frac{\sqrt[4]{a} \sqrt{x} \left(\sqrt{a} \sqrt{c} \left(b^2-20 a c\right)+2 b \left(b^2-8 a c\right)\right) \left(\sqrt{a}+\sqrt{c} x^2\right) \sqrt{\frac{a+b x^2+c x^4}{\left(\sqrt{a}+\sqrt{c} x^2\right)^2}} F\left(2 \tan ^{-1}\left(\frac{\sqrt[4]{c} x}{\sqrt[4]{a}}\right)|\frac{1}{4} \left(2-\frac{b}{\sqrt{a} \sqrt{c}}\right)\right)}{70 c^{7/4} \sqrt{a x+b x^3+c x^5}}+\frac{2 \sqrt[4]{a} b \sqrt{x} \left(b^2-8 a c\right) \left(\sqrt{a}+\sqrt{c} x^2\right) \sqrt{\frac{a+b x^2+c x^4}{\left(\sqrt{a}+\sqrt{c} x^2\right)^2}} E\left(2 \tan ^{-1}\left(\frac{\sqrt[4]{c} x}{\sqrt[4]{a}}\right)|\frac{1}{4} \left(2-\frac{b}{\sqrt{a} \sqrt{c}}\right)\right)}{35 c^{7/4} \sqrt{a x+b x^3+c x^5}}+\frac{\sqrt{x} \left(10 a c+b^2+3 b c x^2\right) \sqrt{a x+b x^3+c x^5}}{35 c}+\frac{\left(a x+b x^3+c x^5\right)^{3/2}}{7 \sqrt{x}}","-\frac{2 b x^{3/2} \left(b^2-8 a c\right) \left(a+b x^2+c x^4\right)}{35 c^{3/2} \left(\sqrt{a}+\sqrt{c} x^2\right) \sqrt{a x+b x^3+c x^5}}-\frac{\sqrt[4]{a} \sqrt{x} \left(\sqrt{a} \sqrt{c} \left(b^2-20 a c\right)+2 b \left(b^2-8 a c\right)\right) \left(\sqrt{a}+\sqrt{c} x^2\right) \sqrt{\frac{a+b x^2+c x^4}{\left(\sqrt{a}+\sqrt{c} x^2\right)^2}} F\left(2 \tan ^{-1}\left(\frac{\sqrt[4]{c} x}{\sqrt[4]{a}}\right)|\frac{1}{4} \left(2-\frac{b}{\sqrt{a} \sqrt{c}}\right)\right)}{70 c^{7/4} \sqrt{a x+b x^3+c x^5}}+\frac{2 \sqrt[4]{a} b \sqrt{x} \left(b^2-8 a c\right) \left(\sqrt{a}+\sqrt{c} x^2\right) \sqrt{\frac{a+b x^2+c x^4}{\left(\sqrt{a}+\sqrt{c} x^2\right)^2}} E\left(2 \tan ^{-1}\left(\frac{\sqrt[4]{c} x}{\sqrt[4]{a}}\right)|\frac{1}{4} \left(2-\frac{b}{\sqrt{a} \sqrt{c}}\right)\right)}{35 c^{7/4} \sqrt{a x+b x^3+c x^5}}+\frac{\sqrt{x} \left(10 a c+b^2+3 b c x^2\right) \sqrt{a x+b x^3+c x^5}}{35 c}+\frac{\left(a x+b x^3+c x^5\right)^{3/2}}{7 \sqrt{x}}",1,"(-2*b*(b^2 - 8*a*c)*x^(3/2)*(a + b*x^2 + c*x^4))/(35*c^(3/2)*(Sqrt[a] + Sqrt[c]*x^2)*Sqrt[a*x + b*x^3 + c*x^5]) + (Sqrt[x]*(b^2 + 10*a*c + 3*b*c*x^2)*Sqrt[a*x + b*x^3 + c*x^5])/(35*c) + (a*x + b*x^3 + c*x^5)^(3/2)/(7*Sqrt[x]) + (2*a^(1/4)*b*(b^2 - 8*a*c)*Sqrt[x]*(Sqrt[a] + Sqrt[c]*x^2)*Sqrt[(a + b*x^2 + c*x^4)/(Sqrt[a] + Sqrt[c]*x^2)^2]*EllipticE[2*ArcTan[(c^(1/4)*x)/a^(1/4)], (2 - b/(Sqrt[a]*Sqrt[c]))/4])/(35*c^(7/4)*Sqrt[a*x + b*x^3 + c*x^5]) - (a^(1/4)*(Sqrt[a]*Sqrt[c]*(b^2 - 20*a*c) + 2*b*(b^2 - 8*a*c))*Sqrt[x]*(Sqrt[a] + Sqrt[c]*x^2)*Sqrt[(a + b*x^2 + c*x^4)/(Sqrt[a] + Sqrt[c]*x^2)^2]*EllipticF[2*ArcTan[(c^(1/4)*x)/a^(1/4)], (2 - b/(Sqrt[a]*Sqrt[c]))/4])/(70*c^(7/4)*Sqrt[a*x + b*x^3 + c*x^5])","A",6,6,24,0.2500,1,"{1921, 1945, 1953, 1197, 1103, 1195}"
113,1,82,0,0.0618114,"\int \frac{x^{3/2}}{\sqrt{a x+b x^3+c x^5}} \, dx","Int[x^(3/2)/Sqrt[a*x + b*x^3 + c*x^5],x]","\frac{\sqrt{x} \sqrt{a+b x^2+c x^4} \tanh ^{-1}\left(\frac{b+2 c x^2}{2 \sqrt{c} \sqrt{a+b x^2+c x^4}}\right)}{2 \sqrt{c} \sqrt{a x+b x^3+c x^5}}","\frac{\sqrt{x} \sqrt{a+b x^2+c x^4} \tanh ^{-1}\left(\frac{b+2 c x^2}{2 \sqrt{c} \sqrt{a+b x^2+c x^4}}\right)}{2 \sqrt{c} \sqrt{a x+b x^3+c x^5}}",1,"(Sqrt[x]*Sqrt[a + b*x^2 + c*x^4]*ArcTanh[(b + 2*c*x^2)/(2*Sqrt[c]*Sqrt[a + b*x^2 + c*x^4])])/(2*Sqrt[c]*Sqrt[a*x + b*x^3 + c*x^5])","A",4,4,24,0.1667,1,"{1914, 1107, 621, 206}"
114,1,121,0,0.0463985,"\int \frac{\sqrt{x}}{\sqrt{a x+b x^3+c x^5}} \, dx","Int[Sqrt[x]/Sqrt[a*x + b*x^3 + c*x^5],x]","\frac{\sqrt{x} \left(\sqrt{a}+\sqrt{c} x^2\right) \sqrt{\frac{a+b x^2+c x^4}{\left(\sqrt{a}+\sqrt{c} x^2\right)^2}} F\left(2 \tan ^{-1}\left(\frac{\sqrt[4]{c} x}{\sqrt[4]{a}}\right)|\frac{1}{4} \left(2-\frac{b}{\sqrt{a} \sqrt{c}}\right)\right)}{2 \sqrt[4]{a} \sqrt[4]{c} \sqrt{a x+b x^3+c x^5}}","\frac{\sqrt{x} \left(\sqrt{a}+\sqrt{c} x^2\right) \sqrt{\frac{a+b x^2+c x^4}{\left(\sqrt{a}+\sqrt{c} x^2\right)^2}} F\left(2 \tan ^{-1}\left(\frac{\sqrt[4]{c} x}{\sqrt[4]{a}}\right)|\frac{1}{4} \left(2-\frac{b}{\sqrt{a} \sqrt{c}}\right)\right)}{2 \sqrt[4]{a} \sqrt[4]{c} \sqrt{a x+b x^3+c x^5}}",1,"(Sqrt[x]*(Sqrt[a] + Sqrt[c]*x^2)*Sqrt[(a + b*x^2 + c*x^4)/(Sqrt[a] + Sqrt[c]*x^2)^2]*EllipticF[2*ArcTan[(c^(1/4)*x)/a^(1/4)], (2 - b/(Sqrt[a]*Sqrt[c]))/4])/(2*a^(1/4)*c^(1/4)*Sqrt[a*x + b*x^3 + c*x^5])","A",2,2,24,0.08333,1,"{1914, 1103}"
115,1,51,0,0.0293618,"\int \frac{1}{\sqrt{x} \sqrt{a x+b x^3+c x^5}} \, dx","Int[1/(Sqrt[x]*Sqrt[a*x + b*x^3 + c*x^5]),x]","-\frac{\tanh ^{-1}\left(\frac{\sqrt{x} \left(2 a+b x^2\right)}{2 \sqrt{a} \sqrt{a x+b x^3+c x^5}}\right)}{2 \sqrt{a}}","-\frac{\tanh ^{-1}\left(\frac{\sqrt{x} \left(2 a+b x^2\right)}{2 \sqrt{a} \sqrt{a x+b x^3+c x^5}}\right)}{2 \sqrt{a}}",1,"-ArcTanh[(Sqrt[x]*(2*a + b*x^2))/(2*Sqrt[a]*Sqrt[a*x + b*x^3 + c*x^5])]/(2*Sqrt[a])","A",2,2,24,0.08333,1,"{1913, 206}"
116,1,330,0,0.1842844,"\int \frac{1}{x^{3/2} \sqrt{a x+b x^3+c x^5}} \, dx","Int[1/(x^(3/2)*Sqrt[a*x + b*x^3 + c*x^5]),x]","\frac{\sqrt[4]{c} \sqrt{x} \left(\sqrt{a}+\sqrt{c} x^2\right) \sqrt{\frac{a+b x^2+c x^4}{\left(\sqrt{a}+\sqrt{c} x^2\right)^2}} F\left(2 \tan ^{-1}\left(\frac{\sqrt[4]{c} x}{\sqrt[4]{a}}\right)|\frac{1}{4} \left(2-\frac{b}{\sqrt{a} \sqrt{c}}\right)\right)}{2 a^{3/4} \sqrt{a x+b x^3+c x^5}}-\frac{\sqrt[4]{c} \sqrt{x} \left(\sqrt{a}+\sqrt{c} x^2\right) \sqrt{\frac{a+b x^2+c x^4}{\left(\sqrt{a}+\sqrt{c} x^2\right)^2}} E\left(2 \tan ^{-1}\left(\frac{\sqrt[4]{c} x}{\sqrt[4]{a}}\right)|\frac{1}{4} \left(2-\frac{b}{\sqrt{a} \sqrt{c}}\right)\right)}{a^{3/4} \sqrt{a x+b x^3+c x^5}}+\frac{\sqrt{c} x^{3/2} \left(a+b x^2+c x^4\right)}{a \left(\sqrt{a}+\sqrt{c} x^2\right) \sqrt{a x+b x^3+c x^5}}-\frac{\sqrt{a x+b x^3+c x^5}}{a x^{3/2}}","\frac{\sqrt[4]{c} \sqrt{x} \left(\sqrt{a}+\sqrt{c} x^2\right) \sqrt{\frac{a+b x^2+c x^4}{\left(\sqrt{a}+\sqrt{c} x^2\right)^2}} F\left(2 \tan ^{-1}\left(\frac{\sqrt[4]{c} x}{\sqrt[4]{a}}\right)|\frac{1}{4} \left(2-\frac{b}{\sqrt{a} \sqrt{c}}\right)\right)}{2 a^{3/4} \sqrt{a x+b x^3+c x^5}}-\frac{\sqrt[4]{c} \sqrt{x} \left(\sqrt{a}+\sqrt{c} x^2\right) \sqrt{\frac{a+b x^2+c x^4}{\left(\sqrt{a}+\sqrt{c} x^2\right)^2}} E\left(2 \tan ^{-1}\left(\frac{\sqrt[4]{c} x}{\sqrt[4]{a}}\right)|\frac{1}{4} \left(2-\frac{b}{\sqrt{a} \sqrt{c}}\right)\right)}{a^{3/4} \sqrt{a x+b x^3+c x^5}}+\frac{\sqrt{c} x^{3/2} \left(a+b x^2+c x^4\right)}{a \left(\sqrt{a}+\sqrt{c} x^2\right) \sqrt{a x+b x^3+c x^5}}-\frac{\sqrt{a x+b x^3+c x^5}}{a x^{3/2}}",1,"(Sqrt[c]*x^(3/2)*(a + b*x^2 + c*x^4))/(a*(Sqrt[a] + Sqrt[c]*x^2)*Sqrt[a*x + b*x^3 + c*x^5]) - Sqrt[a*x + b*x^3 + c*x^5]/(a*x^(3/2)) - (c^(1/4)*Sqrt[x]*(Sqrt[a] + Sqrt[c]*x^2)*Sqrt[(a + b*x^2 + c*x^4)/(Sqrt[a] + Sqrt[c]*x^2)^2]*EllipticE[2*ArcTan[(c^(1/4)*x)/a^(1/4)], (2 - b/(Sqrt[a]*Sqrt[c]))/4])/(a^(3/4)*Sqrt[a*x + b*x^3 + c*x^5]) + (c^(1/4)*Sqrt[x]*(Sqrt[a] + Sqrt[c]*x^2)*Sqrt[(a + b*x^2 + c*x^4)/(Sqrt[a] + Sqrt[c]*x^2)^2]*EllipticF[2*ArcTan[(c^(1/4)*x)/a^(1/4)], (2 - b/(Sqrt[a]*Sqrt[c]))/4])/(2*a^(3/4)*Sqrt[a*x + b*x^3 + c*x^5])","A",6,6,24,0.2500,1,"{1929, 12, 1914, 1139, 1103, 1195}"
117,1,391,0,0.2480593,"\int \frac{x^{3/2}}{\left(a x+b x^3+c x^5\right)^{3/2}} \, dx","Int[x^(3/2)/(a*x + b*x^3 + c*x^5)^(3/2),x]","\frac{b \sqrt[4]{c} \sqrt{x} \left(\sqrt{a}+\sqrt{c} x^2\right) \sqrt{\frac{a+b x^2+c x^4}{\left(\sqrt{a}+\sqrt{c} x^2\right)^2}} E\left(2 \tan ^{-1}\left(\frac{\sqrt[4]{c} x}{\sqrt[4]{a}}\right)|\frac{1}{4} \left(2-\frac{b}{\sqrt{a} \sqrt{c}}\right)\right)}{a^{3/4} \left(b^2-4 a c\right) \sqrt{a x+b x^3+c x^5}}-\frac{\sqrt[4]{c} \sqrt{x} \left(\sqrt{a}+\sqrt{c} x^2\right) \sqrt{\frac{a+b x^2+c x^4}{\left(\sqrt{a}+\sqrt{c} x^2\right)^2}} F\left(2 \tan ^{-1}\left(\frac{\sqrt[4]{c} x}{\sqrt[4]{a}}\right)|\frac{1}{4} \left(2-\frac{b}{\sqrt{a} \sqrt{c}}\right)\right)}{2 a^{3/4} \left(b-2 \sqrt{a} \sqrt{c}\right) \sqrt{a x+b x^3+c x^5}}+\frac{x^{3/2} \left(-2 a c+b^2+b c x^2\right)}{a \left(b^2-4 a c\right) \sqrt{a x+b x^3+c x^5}}-\frac{b \sqrt{c} x^{3/2} \left(a+b x^2+c x^4\right)}{a \left(b^2-4 a c\right) \left(\sqrt{a}+\sqrt{c} x^2\right) \sqrt{a x+b x^3+c x^5}}","\frac{b \sqrt[4]{c} \sqrt{x} \left(\sqrt{a}+\sqrt{c} x^2\right) \sqrt{\frac{a+b x^2+c x^4}{\left(\sqrt{a}+\sqrt{c} x^2\right)^2}} E\left(2 \tan ^{-1}\left(\frac{\sqrt[4]{c} x}{\sqrt[4]{a}}\right)|\frac{1}{4} \left(2-\frac{b}{\sqrt{a} \sqrt{c}}\right)\right)}{a^{3/4} \left(b^2-4 a c\right) \sqrt{a x+b x^3+c x^5}}-\frac{\sqrt[4]{c} \sqrt{x} \left(\sqrt{a}+\sqrt{c} x^2\right) \sqrt{\frac{a+b x^2+c x^4}{\left(\sqrt{a}+\sqrt{c} x^2\right)^2}} F\left(2 \tan ^{-1}\left(\frac{\sqrt[4]{c} x}{\sqrt[4]{a}}\right)|\frac{1}{4} \left(2-\frac{b}{\sqrt{a} \sqrt{c}}\right)\right)}{2 a^{3/4} \left(b-2 \sqrt{a} \sqrt{c}\right) \sqrt{a x+b x^3+c x^5}}+\frac{x^{3/2} \left(-2 a c+b^2+b c x^2\right)}{a \left(b^2-4 a c\right) \sqrt{a x+b x^3+c x^5}}-\frac{b \sqrt{c} x^{3/2} \left(a+b x^2+c x^4\right)}{a \left(b^2-4 a c\right) \left(\sqrt{a}+\sqrt{c} x^2\right) \sqrt{a x+b x^3+c x^5}}",1,"(x^(3/2)*(b^2 - 2*a*c + b*c*x^2))/(a*(b^2 - 4*a*c)*Sqrt[a*x + b*x^3 + c*x^5]) - (b*Sqrt[c]*x^(3/2)*(a + b*x^2 + c*x^4))/(a*(b^2 - 4*a*c)*(Sqrt[a] + Sqrt[c]*x^2)*Sqrt[a*x + b*x^3 + c*x^5]) + (b*c^(1/4)*Sqrt[x]*(Sqrt[a] + Sqrt[c]*x^2)*Sqrt[(a + b*x^2 + c*x^4)/(Sqrt[a] + Sqrt[c]*x^2)^2]*EllipticE[2*ArcTan[(c^(1/4)*x)/a^(1/4)], (2 - b/(Sqrt[a]*Sqrt[c]))/4])/(a^(3/4)*(b^2 - 4*a*c)*Sqrt[a*x + b*x^3 + c*x^5]) - (c^(1/4)*Sqrt[x]*(Sqrt[a] + Sqrt[c]*x^2)*Sqrt[(a + b*x^2 + c*x^4)/(Sqrt[a] + Sqrt[c]*x^2)^2]*EllipticF[2*ArcTan[(c^(1/4)*x)/a^(1/4)], (2 - b/(Sqrt[a]*Sqrt[c]))/4])/(2*a^(3/4)*(b - 2*Sqrt[a]*Sqrt[c])*Sqrt[a*x + b*x^3 + c*x^5])","A",5,5,24,0.2083,1,"{1924, 1953, 1197, 1103, 1195}"
118,1,103,0,0.072923,"\int \frac{\sqrt{x}}{\left(a x+b x^3+c x^5\right)^{3/2}} \, dx","Int[Sqrt[x]/(a*x + b*x^3 + c*x^5)^(3/2),x]","\frac{\sqrt{x} \left(-2 a c+b^2+b c x^2\right)}{a \left(b^2-4 a c\right) \sqrt{a x+b x^3+c x^5}}-\frac{\tanh ^{-1}\left(\frac{\sqrt{x} \left(2 a+b x^2\right)}{2 \sqrt{a} \sqrt{a x+b x^3+c x^5}}\right)}{2 a^{3/2}}","\frac{\sqrt{x} \left(-2 a c+b^2+b c x^2\right)}{a \left(b^2-4 a c\right) \sqrt{a x+b x^3+c x^5}}-\frac{\tanh ^{-1}\left(\frac{\sqrt{x} \left(2 a+b x^2\right)}{2 \sqrt{a} \sqrt{a x+b x^3+c x^5}}\right)}{2 a^{3/2}}",1,"(Sqrt[x]*(b^2 - 2*a*c + b*c*x^2))/(a*(b^2 - 4*a*c)*Sqrt[a*x + b*x^3 + c*x^5]) - ArcTanh[(Sqrt[x]*(2*a + b*x^2))/(2*Sqrt[a]*Sqrt[a*x + b*x^3 + c*x^5])]/(2*a^(3/2))","A",3,3,24,0.1250,1,"{1922, 1913, 206}"
119,1,468,0,0.4086591,"\int \frac{1}{\sqrt{x} \left(a x+b x^3+c x^5\right)^{3/2}} \, dx","Int[1/(Sqrt[x]*(a*x + b*x^3 + c*x^5)^(3/2)),x]","\frac{2 \sqrt{c} x^{3/2} \left(b^2-3 a c\right) \left(a+b x^2+c x^4\right)}{a^2 \left(b^2-4 a c\right) \left(\sqrt{a}+\sqrt{c} x^2\right) \sqrt{a x+b x^3+c x^5}}-\frac{2 \left(b^2-3 a c\right) \sqrt{a x+b x^3+c x^5}}{a^2 x^{3/2} \left(b^2-4 a c\right)}+\frac{\sqrt[4]{c} \sqrt{x} \left(\sqrt{a} b \sqrt{c}-6 a c+2 b^2\right) \left(\sqrt{a}+\sqrt{c} x^2\right) \sqrt{\frac{a+b x^2+c x^4}{\left(\sqrt{a}+\sqrt{c} x^2\right)^2}} F\left(2 \tan ^{-1}\left(\frac{\sqrt[4]{c} x}{\sqrt[4]{a}}\right)|\frac{1}{4} \left(2-\frac{b}{\sqrt{a} \sqrt{c}}\right)\right)}{2 a^{7/4} \left(b^2-4 a c\right) \sqrt{a x+b x^3+c x^5}}-\frac{2 \sqrt[4]{c} \sqrt{x} \left(b^2-3 a c\right) \left(\sqrt{a}+\sqrt{c} x^2\right) \sqrt{\frac{a+b x^2+c x^4}{\left(\sqrt{a}+\sqrt{c} x^2\right)^2}} E\left(2 \tan ^{-1}\left(\frac{\sqrt[4]{c} x}{\sqrt[4]{a}}\right)|\frac{1}{4} \left(2-\frac{b}{\sqrt{a} \sqrt{c}}\right)\right)}{a^{7/4} \left(b^2-4 a c\right) \sqrt{a x+b x^3+c x^5}}+\frac{-2 a c+b^2+b c x^2}{a \sqrt{x} \left(b^2-4 a c\right) \sqrt{a x+b x^3+c x^5}}","\frac{2 \sqrt{c} x^{3/2} \left(b^2-3 a c\right) \left(a+b x^2+c x^4\right)}{a^2 \left(b^2-4 a c\right) \left(\sqrt{a}+\sqrt{c} x^2\right) \sqrt{a x+b x^3+c x^5}}-\frac{2 \left(b^2-3 a c\right) \sqrt{a x+b x^3+c x^5}}{a^2 x^{3/2} \left(b^2-4 a c\right)}+\frac{\sqrt[4]{c} \sqrt{x} \left(\sqrt{a} b \sqrt{c}-6 a c+2 b^2\right) \left(\sqrt{a}+\sqrt{c} x^2\right) \sqrt{\frac{a+b x^2+c x^4}{\left(\sqrt{a}+\sqrt{c} x^2\right)^2}} F\left(2 \tan ^{-1}\left(\frac{\sqrt[4]{c} x}{\sqrt[4]{a}}\right)|\frac{1}{4} \left(2-\frac{b}{\sqrt{a} \sqrt{c}}\right)\right)}{2 a^{7/4} \left(b^2-4 a c\right) \sqrt{a x+b x^3+c x^5}}-\frac{2 \sqrt[4]{c} \sqrt{x} \left(b^2-3 a c\right) \left(\sqrt{a}+\sqrt{c} x^2\right) \sqrt{\frac{a+b x^2+c x^4}{\left(\sqrt{a}+\sqrt{c} x^2\right)^2}} E\left(2 \tan ^{-1}\left(\frac{\sqrt[4]{c} x}{\sqrt[4]{a}}\right)|\frac{1}{4} \left(2-\frac{b}{\sqrt{a} \sqrt{c}}\right)\right)}{a^{7/4} \left(b^2-4 a c\right) \sqrt{a x+b x^3+c x^5}}+\frac{-2 a c+b^2+b c x^2}{a \sqrt{x} \left(b^2-4 a c\right) \sqrt{a x+b x^3+c x^5}}",1,"(b^2 - 2*a*c + b*c*x^2)/(a*(b^2 - 4*a*c)*Sqrt[x]*Sqrt[a*x + b*x^3 + c*x^5]) + (2*Sqrt[c]*(b^2 - 3*a*c)*x^(3/2)*(a + b*x^2 + c*x^4))/(a^2*(b^2 - 4*a*c)*(Sqrt[a] + Sqrt[c]*x^2)*Sqrt[a*x + b*x^3 + c*x^5]) - (2*(b^2 - 3*a*c)*Sqrt[a*x + b*x^3 + c*x^5])/(a^2*(b^2 - 4*a*c)*x^(3/2)) - (2*c^(1/4)*(b^2 - 3*a*c)*Sqrt[x]*(Sqrt[a] + Sqrt[c]*x^2)*Sqrt[(a + b*x^2 + c*x^4)/(Sqrt[a] + Sqrt[c]*x^2)^2]*EllipticE[2*ArcTan[(c^(1/4)*x)/a^(1/4)], (2 - b/(Sqrt[a]*Sqrt[c]))/4])/(a^(7/4)*(b^2 - 4*a*c)*Sqrt[a*x + b*x^3 + c*x^5]) + (c^(1/4)*(2*b^2 + Sqrt[a]*b*Sqrt[c] - 6*a*c)*Sqrt[x]*(Sqrt[a] + Sqrt[c]*x^2)*Sqrt[(a + b*x^2 + c*x^4)/(Sqrt[a] + Sqrt[c]*x^2)^2]*EllipticF[2*ArcTan[(c^(1/4)*x)/a^(1/4)], (2 - b/(Sqrt[a]*Sqrt[c]))/4])/(2*a^(7/4)*(b^2 - 4*a*c)*Sqrt[a*x + b*x^3 + c*x^5])","A",6,6,24,0.2500,1,"{1924, 1951, 1953, 1197, 1103, 1195}"
120,1,154,0,0.1749527,"\int \frac{1}{x^{3/2} \left(a x+b x^3+c x^5\right)^{3/2}} \, dx","Int[1/(x^(3/2)*(a*x + b*x^3 + c*x^5)^(3/2)),x]","-\frac{\left(3 b^2-8 a c\right) \sqrt{a x+b x^3+c x^5}}{2 a^2 x^{5/2} \left(b^2-4 a c\right)}+\frac{3 b \tanh ^{-1}\left(\frac{\sqrt{x} \left(2 a+b x^2\right)}{2 \sqrt{a} \sqrt{a x+b x^3+c x^5}}\right)}{4 a^{5/2}}+\frac{-2 a c+b^2+b c x^2}{a x^{3/2} \left(b^2-4 a c\right) \sqrt{a x+b x^3+c x^5}}","-\frac{\left(3 b^2-8 a c\right) \sqrt{a x+b x^3+c x^5}}{2 a^2 x^{5/2} \left(b^2-4 a c\right)}+\frac{3 b \tanh ^{-1}\left(\frac{\sqrt{x} \left(2 a+b x^2\right)}{2 \sqrt{a} \sqrt{a x+b x^3+c x^5}}\right)}{4 a^{5/2}}+\frac{-2 a c+b^2+b c x^2}{a x^{3/2} \left(b^2-4 a c\right) \sqrt{a x+b x^3+c x^5}}",1,"(b^2 - 2*a*c + b*c*x^2)/(a*(b^2 - 4*a*c)*x^(3/2)*Sqrt[a*x + b*x^3 + c*x^5]) - ((3*b^2 - 8*a*c)*Sqrt[a*x + b*x^3 + c*x^5])/(2*a^2*(b^2 - 4*a*c)*x^(5/2)) + (3*b*ArcTanh[(Sqrt[x]*(2*a + b*x^2))/(2*Sqrt[a]*Sqrt[a*x + b*x^3 + c*x^5])])/(4*a^(5/2))","A",5,5,24,0.2083,1,"{1924, 1951, 12, 1913, 206}"
121,1,51,0,0.0499673,"\int \frac{x^{\frac{3}{2} (-1+n)}}{\left(a x^{-1+n}+b x^n+c x^{1+n}\right)^{3/2}} \, dx","Int[x^((3*(-1 + n))/2)/(a*x^(-1 + n) + b*x^n + c*x^(1 + n))^(3/2),x]","-\frac{2 x^{\frac{n-1}{2}} (b+2 c x)}{\left(b^2-4 a c\right) \sqrt{a x^{n-1}+b x^n+c x^{n+1}}}","-\frac{2 x^{\frac{n-1}{2}} (b+2 c x)}{\left(b^2-4 a c\right) \sqrt{a x^{n-1}+b x^n+c x^{n+1}}}",1,"(-2*x^((-1 + n)/2)*(b + 2*c*x))/((b^2 - 4*a*c)*Sqrt[a*x^(-1 + n) + b*x^n + c*x^(1 + n)])","A",1,1,34,0.02941,1,"{1915}"
122,1,287,0,0.3991775,"\int \frac{x \left(d+e x^2\right)}{\sqrt{a x+b x^3+c x^5}} \, dx","Int[(x*(d + e*x^2))/Sqrt[a*x + b*x^3 + c*x^5],x]","\frac{2 d x^2 \sqrt{\frac{2 c x^2}{b-\sqrt{b^2-4 a c}}+1} \sqrt{\frac{2 c x^2}{\sqrt{b^2-4 a c}+b}+1} F_1\left(\frac{3}{4};\frac{1}{2},\frac{1}{2};\frac{7}{4};-\frac{2 c x^2}{b-\sqrt{b^2-4 a c}},-\frac{2 c x^2}{b+\sqrt{b^2-4 a c}}\right)}{3 \sqrt{a x+b x^3+c x^5}}+\frac{2 e x^4 \sqrt{\frac{2 c x^2}{b-\sqrt{b^2-4 a c}}+1} \sqrt{\frac{2 c x^2}{\sqrt{b^2-4 a c}+b}+1} F_1\left(\frac{7}{4};\frac{1}{2},\frac{1}{2};\frac{11}{4};-\frac{2 c x^2}{b-\sqrt{b^2-4 a c}},-\frac{2 c x^2}{b+\sqrt{b^2-4 a c}}\right)}{7 \sqrt{a x+b x^3+c x^5}}","\frac{2 d x^2 \sqrt{\frac{2 c x^2}{b-\sqrt{b^2-4 a c}}+1} \sqrt{\frac{2 c x^2}{\sqrt{b^2-4 a c}+b}+1} F_1\left(\frac{3}{4};\frac{1}{2},\frac{1}{2};\frac{7}{4};-\frac{2 c x^2}{b-\sqrt{b^2-4 a c}},-\frac{2 c x^2}{b+\sqrt{b^2-4 a c}}\right)}{3 \sqrt{a x+b x^3+c x^5}}+\frac{2 e x^4 \sqrt{\frac{2 c x^2}{b-\sqrt{b^2-4 a c}}+1} \sqrt{\frac{2 c x^2}{\sqrt{b^2-4 a c}+b}+1} F_1\left(\frac{7}{4};\frac{1}{2},\frac{1}{2};\frac{11}{4};-\frac{2 c x^2}{b-\sqrt{b^2-4 a c}},-\frac{2 c x^2}{b+\sqrt{b^2-4 a c}}\right)}{7 \sqrt{a x+b x^3+c x^5}}",1,"(2*d*x^2*Sqrt[1 + (2*c*x^2)/(b - Sqrt[b^2 - 4*a*c])]*Sqrt[1 + (2*c*x^2)/(b + Sqrt[b^2 - 4*a*c])]*AppellF1[3/4, 1/2, 1/2, 7/4, (-2*c*x^2)/(b - Sqrt[b^2 - 4*a*c]), (-2*c*x^2)/(b + Sqrt[b^2 - 4*a*c])])/(3*Sqrt[a*x + b*x^3 + c*x^5]) + (2*e*x^4*Sqrt[1 + (2*c*x^2)/(b - Sqrt[b^2 - 4*a*c])]*Sqrt[1 + (2*c*x^2)/(b + Sqrt[b^2 - 4*a*c])]*AppellF1[7/4, 1/2, 1/2, 11/4, (-2*c*x^2)/(b - Sqrt[b^2 - 4*a*c]), (-2*c*x^2)/(b + Sqrt[b^2 - 4*a*c])])/(7*Sqrt[a*x + b*x^3 + c*x^5])","A",7,4,27,0.1481,1,"{1954, 1335, 1141, 510}"
123,1,45,0,0.0088066,"\int \frac{1}{\sqrt{3 x^2-3 x^4+x^6}} \, dx","Int[1/Sqrt[3*x^2 - 3*x^4 + x^6],x]","-\frac{\tanh ^{-1}\left(\frac{x \left(6-3 x^2\right)}{2 \sqrt{3} \sqrt{x^6-3 x^4+3 x^2}}\right)}{2 \sqrt{3}}","-\frac{\tanh ^{-1}\left(\frac{x \left(6-3 x^2\right)}{2 \sqrt{3} \sqrt{x^6-3 x^4+3 x^2}}\right)}{2 \sqrt{3}}",1,"-ArcTanh[(x*(6 - 3*x^2))/(2*Sqrt[3]*Sqrt[3*x^2 - 3*x^4 + x^6])]/(2*Sqrt[3])","A",2,2,18,0.1111,1,"{1904, 206}"
124,1,45,0,0.0122878,"\int \frac{1}{\sqrt{x^2 \left(3-3 x^2+x^4\right)}} \, dx","Int[1/Sqrt[x^2*(3 - 3*x^2 + x^4)],x]","-\frac{\tanh ^{-1}\left(\frac{x \left(6-3 x^2\right)}{2 \sqrt{3} \sqrt{x^6-3 x^4+3 x^2}}\right)}{2 \sqrt{3}}","-\frac{\tanh ^{-1}\left(\frac{x \left(6-3 x^2\right)}{2 \sqrt{3} \sqrt{x^6-3 x^4+3 x^2}}\right)}{2 \sqrt{3}}",1,"-ArcTanh[(x*(6 - 3*x^2))/(2*Sqrt[3]*Sqrt[3*x^2 - 3*x^4 + x^6])]/(2*Sqrt[3])","A",3,3,18,0.1667,1,"{1996, 1904, 206}"
125,1,45,0,0.0124409,"\int \frac{1}{\sqrt{1-\left(1-x^2\right)^3}} \, dx","Int[1/Sqrt[1 - (1 - x^2)^3],x]","-\frac{\tanh ^{-1}\left(\frac{x \left(6-3 x^2\right)}{2 \sqrt{3} \sqrt{x^6-3 x^4+3 x^2}}\right)}{2 \sqrt{3}}","-\frac{\tanh ^{-1}\left(\frac{x \left(6-3 x^2\right)}{2 \sqrt{3} \sqrt{x^6-3 x^4+3 x^2}}\right)}{2 \sqrt{3}}",1,"-ArcTanh[(x*(6 - 3*x^2))/(2*Sqrt[3]*Sqrt[3*x^2 - 3*x^4 + x^6])]/(2*Sqrt[3])","A",3,3,17,0.1765,1,"{1996, 1904, 206}"
126,1,86,0,0.0413086,"\int \sqrt{3 x^2-3 x^4+x^6} \, dx","Int[Sqrt[3*x^2 - 3*x^4 + x^6],x]","-\frac{\sqrt{x^6-3 x^4+3 x^2} \left(3-2 x^2\right)}{8 x}-\frac{3 \sqrt{x^6-3 x^4+3 x^2} \sinh ^{-1}\left(\frac{3-2 x^2}{\sqrt{3}}\right)}{16 x \sqrt{x^4-3 x^2+3}}","-\frac{\sqrt{x^6-3 x^4+3 x^2} \left(3-2 x^2\right)}{8 x}-\frac{3 \sqrt{x^6-3 x^4+3 x^2} \sinh ^{-1}\left(\frac{3-2 x^2}{\sqrt{3}}\right)}{16 x \sqrt{x^4-3 x^2+3}}",1,"-((3 - 2*x^2)*Sqrt[3*x^2 - 3*x^4 + x^6])/(8*x) - (3*Sqrt[3*x^2 - 3*x^4 + x^6]*ArcSinh[(3 - 2*x^2)/Sqrt[3]])/(16*x*Sqrt[3 - 3*x^2 + x^4])","A",5,5,18,0.2778,1,"{1903, 1107, 612, 619, 215}"
127,1,86,0,0.0420436,"\int \sqrt{x^2 \left(3-3 x^2+x^4\right)} \, dx","Int[Sqrt[x^2*(3 - 3*x^2 + x^4)],x]","-\frac{\sqrt{x^6-3 x^4+3 x^2} \left(3-2 x^2\right)}{8 x}-\frac{3 \sqrt{x^6-3 x^4+3 x^2} \sinh ^{-1}\left(\frac{3-2 x^2}{\sqrt{3}}\right)}{16 x \sqrt{x^4-3 x^2+3}}","-\frac{\sqrt{x^6-3 x^4+3 x^2} \left(3-2 x^2\right)}{8 x}-\frac{3 \sqrt{x^6-3 x^4+3 x^2} \sinh ^{-1}\left(\frac{3-2 x^2}{\sqrt{3}}\right)}{16 x \sqrt{x^4-3 x^2+3}}",1,"-((3 - 2*x^2)*Sqrt[3*x^2 - 3*x^4 + x^6])/(8*x) - (3*Sqrt[3*x^2 - 3*x^4 + x^6]*ArcSinh[(3 - 2*x^2)/Sqrt[3]])/(16*x*Sqrt[3 - 3*x^2 + x^4])","A",6,6,18,0.3333,1,"{1996, 1903, 1107, 612, 619, 215}"
128,1,86,0,0.0411441,"\int \sqrt{1-\left(1-x^2\right)^3} \, dx","Int[Sqrt[1 - (1 - x^2)^3],x]","-\frac{\sqrt{x^6-3 x^4+3 x^2} \left(3-2 x^2\right)}{8 x}-\frac{3 \sqrt{x^6-3 x^4+3 x^2} \sinh ^{-1}\left(\frac{3-2 x^2}{\sqrt{3}}\right)}{16 x \sqrt{x^4-3 x^2+3}}","-\frac{\sqrt{x^6-3 x^4+3 x^2} \left(3-2 x^2\right)}{8 x}-\frac{3 \sqrt{x^6-3 x^4+3 x^2} \sinh ^{-1}\left(\frac{3-2 x^2}{\sqrt{3}}\right)}{16 x \sqrt{x^4-3 x^2+3}}",1,"-((3 - 2*x^2)*Sqrt[3*x^2 - 3*x^4 + x^6])/(8*x) - (3*Sqrt[3*x^2 - 3*x^4 + x^6]*ArcSinh[(3 - 2*x^2)/Sqrt[3]])/(16*x*Sqrt[3 - 3*x^2 + x^4])","A",6,6,17,0.3529,1,"{1996, 1903, 1107, 612, 619, 215}"
129,1,38,0,0.0158717,"\int \frac{1}{x \sqrt{a+b x+c x^2}} \, dx","Int[1/(x*Sqrt[a + b*x + c*x^2]),x]","-\frac{\tanh ^{-1}\left(\frac{2 a+b x}{2 \sqrt{a} \sqrt{a+b x+c x^2}}\right)}{\sqrt{a}}","-\frac{\tanh ^{-1}\left(\frac{2 a+b x}{2 \sqrt{a} \sqrt{a+b x+c x^2}}\right)}{\sqrt{a}}",1,"-(ArcTanh[(2*a + b*x)/(2*Sqrt[a]*Sqrt[a + b*x + c*x^2])]/Sqrt[a])","A",2,2,18,0.1111,1,"{724, 206}"
130,1,45,0,0.0216179,"\int \frac{1}{\sqrt{x^2 \left(a+b x+c x^2\right)}} \, dx","Int[1/Sqrt[x^2*(a + b*x + c*x^2)],x]","-\frac{\tanh ^{-1}\left(\frac{x (2 a+b x)}{2 \sqrt{a} \sqrt{a x^2+b x^3+c x^4}}\right)}{\sqrt{a}}","-\frac{\tanh ^{-1}\left(\frac{x (2 a+b x)}{2 \sqrt{a} \sqrt{a x^2+b x^3+c x^4}}\right)}{\sqrt{a}}",1,"-(ArcTanh[(x*(2*a + b*x))/(2*Sqrt[a]*Sqrt[a*x^2 + b*x^3 + c*x^4])]/Sqrt[a])","A",3,3,18,0.1667,1,"{1996, 1904, 206}"
131,1,47,0,0.0756258,"\int \frac{1}{\sqrt{x} \sqrt{x \left(a+b x+c x^2\right)}} \, dx","Int[1/(Sqrt[x]*Sqrt[x*(a + b*x + c*x^2)]),x]","-\frac{\tanh ^{-1}\left(\frac{\sqrt{x} (2 a+b x)}{2 \sqrt{a} \sqrt{a x+b x^2+c x^3}}\right)}{\sqrt{a}}","-\frac{\tanh ^{-1}\left(\frac{\sqrt{x} (2 a+b x)}{2 \sqrt{a} \sqrt{a x+b x^2+c x^3}}\right)}{\sqrt{a}}",1,"-(ArcTanh[(Sqrt[x]*(2*a + b*x))/(2*Sqrt[a]*Sqrt[a*x + b*x^2 + c*x^3])]/Sqrt[a])","A",3,3,22,0.1364,1,"{1997, 1913, 206}"
132,1,49,0,0.0899707,"\int \frac{\sqrt{x}}{\sqrt{x^3 \left(a+b x+c x^2\right)}} \, dx","Int[Sqrt[x]/Sqrt[x^3*(a + b*x + c*x^2)],x]","-\frac{\tanh ^{-1}\left(\frac{x^{3/2} (2 a+b x)}{2 \sqrt{a} \sqrt{a x^3+b x^4+c x^5}}\right)}{\sqrt{a}}","-\frac{\tanh ^{-1}\left(\frac{x^{3/2} (2 a+b x)}{2 \sqrt{a} \sqrt{a x^3+b x^4+c x^5}}\right)}{\sqrt{a}}",1,"-(ArcTanh[(x^(3/2)*(2*a + b*x))/(2*Sqrt[a]*Sqrt[a*x^3 + b*x^4 + c*x^5])]/Sqrt[a])","A",3,3,24,0.1250,1,"{1997, 1913, 206}"
133,1,44,0,0.0357734,"\int \frac{1}{x \sqrt{a+b x^2+c x^4}} \, dx","Int[1/(x*Sqrt[a + b*x^2 + c*x^4]),x]","-\frac{\tanh ^{-1}\left(\frac{2 a+b x^2}{2 \sqrt{a} \sqrt{a+b x^2+c x^4}}\right)}{2 \sqrt{a}}","-\frac{\tanh ^{-1}\left(\frac{2 a+b x^2}{2 \sqrt{a} \sqrt{a+b x^2+c x^4}}\right)}{2 \sqrt{a}}",1,"-ArcTanh[(2*a + b*x^2)/(2*Sqrt[a]*Sqrt[a + b*x^2 + c*x^4])]/(2*Sqrt[a])","A",3,3,20,0.1500,1,"{1114, 724, 206}"
134,1,49,0,0.0151489,"\int \frac{1}{\sqrt{x^2 \left(a+b x^2+c x^4\right)}} \, dx","Int[1/Sqrt[x^2*(a + b*x^2 + c*x^4)],x]","-\frac{\tanh ^{-1}\left(\frac{x \left(2 a+b x^2\right)}{2 \sqrt{a} \sqrt{a x^2+b x^4+c x^6}}\right)}{2 \sqrt{a}}","-\frac{\tanh ^{-1}\left(\frac{x \left(2 a+b x^2\right)}{2 \sqrt{a} \sqrt{a x^2+b x^4+c x^6}}\right)}{2 \sqrt{a}}",1,"-ArcTanh[(x*(2*a + b*x^2))/(2*Sqrt[a]*Sqrt[a*x^2 + b*x^4 + c*x^6])]/(2*Sqrt[a])","A",3,3,20,0.1500,1,"{1996, 1904, 206}"
135,1,51,0,0.0672684,"\int \frac{1}{\sqrt{x} \sqrt{x \left(a+b x^2+c x^4\right)}} \, dx","Int[1/(Sqrt[x]*Sqrt[x*(a + b*x^2 + c*x^4)]),x]","-\frac{\tanh ^{-1}\left(\frac{\sqrt{x} \left(2 a+b x^2\right)}{2 \sqrt{a} \sqrt{a x+b x^3+c x^5}}\right)}{2 \sqrt{a}}","-\frac{\tanh ^{-1}\left(\frac{\sqrt{x} \left(2 a+b x^2\right)}{2 \sqrt{a} \sqrt{a x+b x^3+c x^5}}\right)}{2 \sqrt{a}}",1,"-ArcTanh[(Sqrt[x]*(2*a + b*x^2))/(2*Sqrt[a]*Sqrt[a*x + b*x^3 + c*x^5])]/(2*Sqrt[a])","A",3,3,24,0.1250,1,"{1997, 1913, 206}"
136,1,53,0,0.0772904,"\int \frac{\sqrt{x}}{\sqrt{x^3 \left(a+b x^2+c x^4\right)}} \, dx","Int[Sqrt[x]/Sqrt[x^3*(a + b*x^2 + c*x^4)],x]","-\frac{\tanh ^{-1}\left(\frac{x^{3/2} \left(2 a+b x^2\right)}{2 \sqrt{a} \sqrt{a x^3+b x^5+c x^7}}\right)}{2 \sqrt{a}}","-\frac{\tanh ^{-1}\left(\frac{x^{3/2} \left(2 a+b x^2\right)}{2 \sqrt{a} \sqrt{a x^3+b x^5+c x^7}}\right)}{2 \sqrt{a}}",1,"-ArcTanh[(x^(3/2)*(2*a + b*x^2))/(2*Sqrt[a]*Sqrt[a*x^3 + b*x^5 + c*x^7])]/(2*Sqrt[a])","A",3,3,26,0.1154,1,"{1997, 1913, 206}"
137,1,40,0,0.0268767,"\int \frac{1}{x \sqrt{3-3 x^2+x^4}} \, dx","Int[1/(x*Sqrt[3 - 3*x^2 + x^4]),x]","-\frac{\tanh ^{-1}\left(\frac{\sqrt{3} \left(2-x^2\right)}{2 \sqrt{x^4-3 x^2+3}}\right)}{2 \sqrt{3}}","-\frac{\tanh ^{-1}\left(\frac{\sqrt{3} \left(2-x^2\right)}{2 \sqrt{x^4-3 x^2+3}}\right)}{2 \sqrt{3}}",1,"-ArcTanh[(Sqrt[3]*(2 - x^2))/(2*Sqrt[3 - 3*x^2 + x^4])]/(2*Sqrt[3])","A",3,3,18,0.1667,1,"{1114, 724, 206}"
138,1,45,0,0.0119649,"\int \frac{1}{\sqrt{x^2 \left(3-3 x^2+x^4\right)}} \, dx","Int[1/Sqrt[x^2*(3 - 3*x^2 + x^4)],x]","-\frac{\tanh ^{-1}\left(\frac{x \left(6-3 x^2\right)}{2 \sqrt{3} \sqrt{x^6-3 x^4+3 x^2}}\right)}{2 \sqrt{3}}","-\frac{\tanh ^{-1}\left(\frac{x \left(6-3 x^2\right)}{2 \sqrt{3} \sqrt{x^6-3 x^4+3 x^2}}\right)}{2 \sqrt{3}}",1,"-ArcTanh[(x*(6 - 3*x^2))/(2*Sqrt[3]*Sqrt[3*x^2 - 3*x^4 + x^6])]/(2*Sqrt[3])","A",3,3,18,0.1667,1,"{1996, 1904, 206}"
139,1,43,0,0.0474514,"\int \frac{1}{\sqrt{x} \sqrt{x \left(3-3 x+x^2\right)}} \, dx","Int[1/(Sqrt[x]*Sqrt[x*(3 - 3*x + x^2)]),x]","-\frac{\tanh ^{-1}\left(\frac{\sqrt{3} (2-x) \sqrt{x}}{2 \sqrt{x^3-3 x^2+3 x}}\right)}{\sqrt{3}}","-\frac{\tanh ^{-1}\left(\frac{\sqrt{3} (2-x) \sqrt{x}}{2 \sqrt{x^3-3 x^2+3 x}}\right)}{\sqrt{3}}",1,"-(ArcTanh[(Sqrt[3]*(2 - x)*Sqrt[x])/(2*Sqrt[3*x - 3*x^2 + x^3])]/Sqrt[3])","A",3,3,20,0.1500,1,"{1997, 1913, 206}"
140,1,70,0,0.0666428,"\int \frac{x^{-1+\frac{q}{2}}}{\sqrt{b x^n+c x^{2 n-q}+a x^q}} \, dx","Int[x^(-1 + q/2)/Sqrt[b*x^n + c*x^(2*n - q) + a*x^q],x]","-\frac{\tanh ^{-1}\left(\frac{x^{q/2} \left(2 a+b x^{n-q}\right)}{2 \sqrt{a} \sqrt{a x^q+b x^n+c x^{2 n-q}}}\right)}{\sqrt{a} (n-q)}","-\frac{\tanh ^{-1}\left(\frac{x^{q/2} \left(2 a+b x^{n-q}\right)}{2 \sqrt{a} \sqrt{a x^q+b x^n+c x^{2 n-q}}}\right)}{\sqrt{a} (n-q)}",1,"-(ArcTanh[(x^(q/2)*(2*a + b*x^(n - q)))/(2*Sqrt[a]*Sqrt[b*x^n + c*x^(2*n - q) + a*x^q])]/(Sqrt[a]*(n - q)))","A",2,2,36,0.05556,1,"{1913, 206}"